The angle of elevation from me to the top of a hill is 51 degrees. The angle of elevation from me to the top of a tree is 57 degrees. The tree stands 20 ft off the hill. How high is the top of the tree from the base of the hill?
Answers
Answer:
Approximately [tex]101\; \rm ft[/tex] (assuming that the height of the base of the hill is the same as that of the observer.)
Step-by-step explanation:
Refer to the diagram attached.
Let [tex]\rm O[/tex] denote the observer.Let [tex]\rm A[/tex] denote the top of the tree.Let [tex]\rm R[/tex] denote the base of the tree.Let [tex]\rm B[/tex] denote the point where line [tex]\rm AR[/tex] (a vertical line) and the horizontal line going through [tex]\rm O[/tex] meets. [tex]\angle \rm B\hat{A}R = 90^\circ[/tex].Angles:
Angle of elevation of the base of the tree as it appears to the observer: [tex]\angle \rm B\hat{O}R = 51^\circ[/tex].Angle of elevation of the top of the tree as it appears to the observer: [tex]\angle \rm B\hat{O}A = 57^\circ[/tex].
Let the length of segment [tex]\rm BR[/tex] (vertical distance between the base of the tree and the base of the hill) be [tex]x\; \rm ft[/tex].
The question is asking for the length of segment [tex]\rm AB[/tex]. Notice that the length of this segment is [tex]\mathrm{AB} = (x + 20)\; \rm ft[/tex].
The length of segment [tex]\rm OB[/tex] could be represented in two ways:
In right triangle [tex]\rm \triangle OBR[/tex] as the side adjacent to [tex]\angle \rm B\hat{O}R = 51^\circ[/tex].In right triangle [tex]\rm \triangle OBA[/tex] as the side adjacent to [tex]\angle \rm B\hat{O}A = 57^\circ[/tex].For example, in right triangle [tex]\rm \triangle OBR[/tex], the length of the side opposite to [tex]\angle \rm B\hat{O}R = 51^\circ[/tex] is segment [tex]\rm BR[/tex]. The length of that segment is [tex]x\; \rm ft[/tex].
[tex]\begin{aligned}\tan{\left(\angle\mathrm{B\hat{O}R}\right)} = \frac{\,\rm {BR}\,}{\,\rm {OB}\,} \; \genfrac{}{}{0em}{}{\leftarrow \text{opposite}}{\leftarrow \text{adjacent}}\end{aligned}[/tex].
Rearrange to find an expression for the length of [tex]\rm OB[/tex] (in [tex]\rm ft[/tex]) in terms of [tex]x[/tex]:
[tex]\begin{aligned}\mathrm{OB} &= \frac{\mathrm{BR}}{\tan{\left(\angle\mathrm{B\hat{O}R}\right)}} \\ &= \frac{x}{\tan\left(51^\circ\right)}\approx 0.810\, x\end{aligned}[/tex].
Similarly, in right triangle [tex]\rm \triangle OBA[/tex]:
[tex]\begin{aligned}\mathrm{OB} &= \frac{\mathrm{AB}}{\tan{\left(\angle\mathrm{B\hat{O}A}\right)}} \\ &= \frac{x + 20}{\tan\left(57^\circ\right)}\approx 0.649\, (x + 20)\end{aligned}[/tex].
Equate the right-hand side of these two equations:
[tex]0.810\, x \approx 0.649\, (x + 20)[/tex].
Solve for [tex]x[/tex]:
[tex]x \approx 81\; \rm ft[/tex].
Hence, the height of the top of this tree relative to the base of the hill would be [tex](x + 20)\; {\rm ft}\approx 101\; \rm ft[/tex].
Related Questions
Find the value of x and the values of the missing angles. 12 points!
Answers
Answer:
X=30
Step-by-step explanation:
4x+x+x=6x 180/6=30 so 4x= 120
x on the bottom left is just 30 and x on the right is 30x3
There are eight nickels and five dimes in your pocket. You randomly pick a coin out of your pocket and then return it to your pocket. Then you randomly pick another coin. Both times the coin is a nickel.
Answers
Which expression is equivalent to 6-(-8)?
-6+8
-6+(-3)
6+(-8)
6 + 8
Answers
Answer:
6+8 becuase -(-8) = +8
Step-by-step explanation:
On a field trip, there are 3 chaperones for every 20 students. There are 92 people on the trip. Answer these questions. If you get stuck, consider using a tape diagram.
Answers
Answer:
I don't really know what the question is but..
Step-by-step explanation:
Since total of 92 people in the trip including student and chaperon, add groups of 23 to become 92 or use this equation
(20+3)xy=92
23y=92
y=92/23
y=4
therefore,
20x4=80 (students)
3x4=12 (chaperons)
Answer:
15 chaperones
Step-by-step explanation:
1. Okay, First you're going to see how many times 20 can feet into 92. Which is 4.5 times. However, you cannot cut someone in half. So the answer would actually be 5. Then. Just do 5*3, because remember, there are THREE chaperones for every 20 students.
(-2/3)+3/4 Please help
Answers
Answer:
-17\12
Step-by-step explanation:
n automobile manufacturer claims that its van has a 37.4 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating. After testing 280 vans, they found a mean MPG of 37.8. Assume the standard deviation is known to be 2.3. A level of significance of 0.05 will be used. Find the value of the test statistic. Round your answer to 2 decimal places.
Answers
Answer:
Then z(s) is out of the acceptance region, we reject H₀, doubts of the independent testing firm are valids
Step-by-step explanation:
We will develop a Hypothesis Test ( a 2 tail test since the independent testing firm is interested in finding out if there is an incorrect MPG rating from the manufacturer
Test Hypothesis :
Null hypothesis H₀ μ = μ₀
Alternative Hypothesis Hₐ μ ≠ μ₀
Significance Level α = 0,05 α/2 = 0,025
z(c) for α/2 from z-table z(c) = - 1, 96 and by symmetry z(c) = 1,96
Calculating z(s)
z(s) = ( μ - μ₀ ) / σ /√n
z(s) = ( 37,8 - 37,4 ) / 2,3 /√280
z(s) = 0,4 * 16,73 / 2,3
z(s) = 2,90
Comparison between z(c) and z(s)
z(s) > z(c) 2,90 > 1,96
Then z(s) is out of the acceptance region, we reject H₀, doubts of the independent testing firm are valids
The following shape is a rhombus. Find the measure of each unknown angle:
90
52
38
46
72
Answers
Answer:
63 42
53
53
52
Jdjdjdjfh
Properties of a rhombus:Diagonals of a rhombus intersect each other at 90°. Sum of two adjacent angles of a rhombus is 180°.Diagonals bisect opposite angles.
By using property - 1,
m∠APD = m∠DPC = m∠BPC = m∠APB = 90°
Apply triangle sum theorem in ΔAPD,
m∠DAP + m∠APD + m∠DPA = 180°
52° + 90°+ m∠DPA = 180°
m∠DPA = 38°
By using property - 3,
m∠PDC = m∠DPA = 38°
m∠PAB = 52°
By using property - 2,
m∠ADC + m∠DCB = 180°
2(38°) + m∠DCB = 180°
m∠DCB = 104°
Therefore, m∠PCD = m∠PCB = [tex]\frac{104}{2}[/tex] = 52°
m∠DAP = m∠BAP = 52°
Since, m∠ADC = m∠ABC = 76°
Therefore, mABP = m∠CBP = [tex]\frac{76}{2}=38^\circ[/tex]
Hence, m∠APD = m∠DPC = m∠BPC = m∠APB = 90°, m∠DPA = 38°, m∠PAB = 52°, m∠PCD = m∠PCB = 52°, m∠BAP = 52°, mABP = m∠CBP = 38°.
Learn more about rhombus here,
https://brainly.com/question/11812488?referrer=searchResults
which statements are true about points A, B, and C? check all that apply.
Answers
Answer:
2
Step-by-step explanation:
2 seems to be the only one that is correct
Correct Statements: (modified the statements that are incorrect)
1. The coordinates of point A are (-3, 3)
2. Already correct
3. The coordinates of point C are (-2, -2)
4. Point B is the closest to the y-axis (only one away)
5. Point A is 3 away and Point B is 1 away
(sorry if this is confusing but this is what I got)
plz i need help with this
Answers
Answer:
congruence, corresponding,sum of 180
Let n1=50, X1=10, n2=50, and X2=30. Complete parts (a) and (b) below. a. At the 0.10 level of significance, is there evidence of a significant difference between the two population proportions? Determine the null and alternative hypotheses. Choose the correct answer below. A. H0: π1≤π2 H1: π1>π2 B. H0: π1≠π2 H1: π1=π2 C. H0: π1≥π2 H1: π1<π2 D. H0: π1=π2 H1: π1≠π2 Your answer is correct. Calculate the test statistic, ZSTAT, based on the difference p1−p2. The test statistic, ZSTAT, is nothing.
Answers
Answer:
|Z| = |-4.089| > 1.645 at 0.10 level of significance
Null hypothesis is rejected at 0.10 level of significance
There is a difference between the two Population proportions
Step-by-step explanation:
Step(i):-
Given first sample size (n₁) = 50
Given proportion of the first sample p⁻₁= 0.2
Given second sample size (n₂) = 50
Given proportion of the second sample p₂⁻ = 30/50 = 0.6
Null Hypothesis : H₀: p₁⁻=p₂⁻
Alternative Hypothesis : H₁: p₁⁻≠p₂⁻
Step(ii):-
Z-statistic
[tex]Z = \frac{p_{1} -p_{2} }{\sqrt{pq(\frac{1}{n_{1} } +\frac{1}{n_{2}) } } }[/tex]
Where
[tex]P = \frac{n_{1}p_{1} +n_{2} p_{2} }{n_{1} +n_{2} }[/tex]
[tex]P = \frac{50X0.2+50X0.6}{50+50} = 0.4[/tex]
Z-statistic
[tex]Z = \frac{0.2-0.6}{\sqrt{0.4 X 0.6(\frac{1}{50}+\frac{1}{50} } }[/tex]
Z = -4.089
Level of significance =0.10
Z₀.₁₀ = 1.645
|Z| = |-4.089| > 1.645 at 0.10 level of significance
Null hypothesis is rejected at 0.10 level of significance
Final answer:-
There is a difference between the two Population proportions
Please answer this correctly fast!! What type of triangle is this?
Options:
- SSS
- SAS
- ASA
- AAS
- HL
- Not Possible
Answers
Answer:
Not possible
Step-by-step explanation:
These triangles are not congruent
Consider the function represented by the equation x – y = 3. What is the equation written in function notation, with x as the independent variable? f(x) = y + 3 f(x) = –y – 3 f(x) = –x + 3 f(x) = x – 3 ANSWER WITHIN 1O MINUTES AND WILL GIVE BRAINLIEST
Answers
Answer:
d
Step-by-step explanation:
Answer:
the answer is D i think.
True or False? A circle could be circumscribed about the quadrilateral below.
OA. True
OB. False
Answers
Answer:
True
Step-by-step explanation:
The solution is, OA. True, A circle could be circumscribed about the quadrilateral below.
What is circle?A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. The perimeter around the circle is known as the circumference.
here, we have,
from the given diagram, we get,
the angles of each side = 90 degree
and, as per shape, it is a rectangle.
now, we know that,
If opposite angles of a quadrilateral add to 180 then it is called a cyclic quadrilateral and a circle can be inscribed in it.
now, we get,
Here, the opposite sides are 90 and 90 (=180),
so, we have,
which means that it is true that a circle can be circumscribed about the quadrilateral above.
Hence, The solution is, OA. True, A circle could be circumscribed about the quadrilateral below.
Learn more about circle here:
brainly.com/question/11833983
#SPJ5
The following list gives the number of public libraries in each of 11 cities. 12, 3, 5, 4, 7, 8, 11, 13, 10, 6, 2 Find the modes of this data set. If there is more than one mode, write them separated by commas. If there is no mode, click on "No mode."
Answers
Round 259.98991 to the nearest hundredths
Answers
Answer:
259.99
Step-by-step explanation:
You look at the hundreths place and see if the number behind it is bigger than 5, and if it is then you up it by one, and if it's 4 and below then you round it to zero. In this case you up it by one and you get 269.99.
I hope this helps!!!!
Answer:
hey
Step-by-step explanation:
259.99................................................................
wow
PLEASE HURRY
What is the gross earnings for a person who has $30,000 in total sales, $2250 in Returns and Allowances, and a rate of commission of 6%?
Answers
Answer:
$1800
Step-by-step explanation:
$30000x.06=1800
Answer:
I believe the answer is 1,800
Step-by-step explanation:
I could be wrong but hope this helps :)
A Chromebook costs $249.99 at Target. On Black Friday, it is on sale for 15% off.
What is the price of the computer on Black Friday?
Answers
With original price $249.99 and 15% off,
Final price: $212.49
Saved amount: $37.50
Answer:
nah
Step-by-step explanation:
asdddddddddddddddddddddddddddddddddddddddddddddd
Apollo Spas services 156 hot tubs. If each hot tub needs 105 mL of muriatic acid, how many liters of acid are needed for all of the hot tubs?
Answers
Answer:
16380 mL or 16.380 L
Step-by-step explanation:
1 hot tub requires 105 mL of Acid
156 hot tubs requires 105 * 156 mL of acid = 16380 mL of acid are needed.
16380 / 1000 mL/L = 16.380 Liters.
Find the sum. 54.703 + 298.1
Answers
Assume the birth of a boy or a girl is equally likely. The probability that a single child is born a girl is One-half. What is the probability that the next child born to the same familiy will also be a girl?
a.
One-half
b.
One-fourth
c.
StartFraction 1 Over 8 EndFraction
d.
StartFraction 1 Over 12 EndFraction
Answers
Answer:
B
Step-by-step explanation:
EDG2021
10. What is the area of a triangle with base 4cm and
height 8cm?
A. 6cm2 B. 9cm2 C. 14cm D. 16 cm
Answers
Step-by-step explanation:
Area of triangle = 0.5(4)(8) = 16cm² (D).
which sentence contains a metapohor?
Answers
Answer:
The last one
Step-by-step explanation:
its comparing 2 things without using like or as
Answer:
The park road would be a black ribbon rippling through the majestic landscape
I'm pretty sure :)
Step-by-step explanation:
need help please, i don’t get it
Answers
This is the same as saying x = 3 and x = 7.
========================================
Work Shown:
Plug x = 3 into f(x)
f(x) = (1/2)*|x-3| + 3
f(3) = (1/2)*|3-3| + 3
f(3) = 0.5*|0| + 3
f(3) = 0.5*0 + 3
f(3) = 0 + 3
f(3) = 3
-----------------------
Plug x = 5 into f(x)
f(x) = (1/2)*|x-3| + 3
f(5) = (1/2)*|5-3| + 3
f(5) = 0.5*|2| + 3
f(5) = 0.5*2 + 3
f(5) = 1 + 3
f(5) = 4
-----------------------
Plug x = 7 into f(x)
f(x) = (1/2)*|x-3| + 3
f(7) = (1/2)*|7-3| + 3
f(7) = 0.5*|4| + 3
f(7) = 0.5*4 + 3
f(7) = 2 + 3
f(7) = 5
-----------------------
Plug x = 3 into g(x)
g(x) = sqrt(x-3) + 3
g(3) = sqrt(3-3) + 3
g(3) = sqrt(0) + 3
g(3) = 0 + 3
g(3) = 3
-----------------------
Plug x = 5 into g(x)
g(x) = sqrt(x-3) + 3
g(5) = sqrt(5-3) + 3
g(5) = sqrt(2) + 3
g(5) = 1.414214 + 3
g(5) = 4.414214 ..... which is approximate
-----------------------
Plug x = 7 into g(x)
g(x) = sqrt(x-3) + 3
g(7) = sqrt(7-3) + 3
g(7) = sqrt(4) + 3
g(7) = 2 + 3
g(7) = 5
-----------------------
To summarize everything, refer to the table below.
The rows highlighted in yellow refer to when f(x) = g(x)
This happens twice when x = 3 and x = 7
If x = 3, then f(x) = g(x) = 3
If x = 7, then f(x) = g(x) = 5
Therefore, x = 3 and x = 7 are two solutions to f(x) = g(x)
The owner of a golf course wants to determine if his golf course is more difficult than the one his friend owns. He has 20 golfers play a round of 18 holes on his golf course and records their scores. Later that week, he has the same 20 golfers play a round of golf on his friend's course and records their scores again. The average difference in the scores (treated as the scores on his course - the scores on his friend's course) is 8.9 and the standard deviation of the differences are 11.986. Calculate a 99% confidence interval to estimate the average difference in scores between the two courses.
Answers
Answer:
(1.985, 15.815)
Step-by-step explanation:
Given that:
Sample size (n) = 20
Standard deviation (s) = 11.986
Mean (m) = 8.9
α = 99%
Using the relation :
Confidence Interval = Mean ± Error
Where ;
Error = Zcritical * standard deviation / sqrt(n)
Zcritical at 99% = 2.58
Hence,
Error = 2.58 * (11.986/sqrt(20))
Error = 2.58 * 2.6801510
Error = 6.91478958
Hence,
Lower boundary = 8.9 - 6.91478958 = 1.98521042
Upper boundary = 8.9 + 6.91478958 = 15.81478958
(1.985, 15.815)
Using the Zero Product Property identify the solution set for (x + 3) (x + 8) = 0
a. -3, 8
b. -3, -8
c. 3, 8
d. 3, -8
Answers
7+2x/4=5 i ll mark the brailliest
Answers
Your expression is a little unclear, but I am assuming your expression as:
[tex]7+\frac{2x}{4}=5[/tex]
The solution would still clear your concept in anyway.
Answer:
The value of x = -4
Step-by-step explanation:
Given the expression
[tex]7+\frac{2x}{4}=5[/tex]
solving the expression
[tex]7+\frac{2x}{4}=5[/tex]
as 2x/4 = x/2, so
[tex]7+\frac{x}{2}=5[/tex]
subtract 7 from both sides
[tex]7+\frac{x}{2}-7=5-7[/tex]
simplify
[tex]\frac{x}{2}=-2[/tex]
Multiply both sides by 2
[tex]\frac{2x}{2}=2\left(-2\right)[/tex]
simplify
[tex]x=-4[/tex]
Thus, the value of x = -4
Jonas earns tips serving customers in a restaurant. He uses a certain method to correctly determine a tip of 20% of the cost of a meal. If c is the cost of a meal, which of the following can be the method Jonas uses?
A.
Move the decimal point two places to the right, and then double that amount.
B.
Move the decimal point one place to the right, and then double that amount.
C.
Move the decimal point two places to the left, and then double that amount.
D.
Move the decimal point one place to the left, and then double that amount.
Answers
Answer:
b
Step-by-step explanation:
A box contains 1 3/4 Pasta how many ounces of pasta are in the box
Answers
Answer:
Step-by-step explanation:
is there more information to the question??
how many ways can 3 yearbooo posters out of a total of 6 posters be displayed across a wall?
Answers
Answer:
69
Step-by-step explanation:
Jo got 16 out of 20 on her test. What is Jo's grade? Did she pass? Explain how you got your answer.
Answers
Answer:
16/20 is 80
Step-by-step explanation:
What is the number that JO would pass at. I think Jo has passed and I got my answer because when u do 16 divided by 20 you get 0.8 and that is 80
