Triangle ABC has AB = 10 √3cm, AC=6cm and has area 45cm^2
(i) Find the size of angle CAB.
(ii) Find the length of BC
Answers
Answer:
I) ∠CAB measures 60°.
II) BC measures approximately 15.23 cm.
*Please read notes.
Step-by-step explanation:
We are given ΔABC, where AB measures 10√3 cm, AC measures 6 cm, and the triangle has an area of 45 square cm.
And we want to find I) the measure of ∠CAB and II) the length of BC.
I) First, we should always draw a representative triangle so we can determine the sides and angles. This is shown below.
Note that ∠CAB (or simply ∠A) is the angle between the two sides. Thus, we can find the angle by using the alternative formula for the area of a triangle:
[tex]\displaystyle A=\frac{1}{2}ab\sin(C)[/tex]
Where a and b are two side lengths, and C is the angle between the two sides.
Substitute:
[tex]\displaystyle 45=\frac{1}{2}(10\sqrt{3})(6)\sin(A)[/tex]
Simplify:
[tex]\displaystyle 45=30\sqrt{3}\sin(A)[/tex]
So:
[tex]\displaystyle \sin(A)=\frac{45}{30\sqrt{3}}=\frac{3}{2\sqrt3}=\frac{\sqrt{3}}{2}[/tex]
Take the inverse sine of both sides. Use a calculator. Thus:
[tex]\displaystyle m\angle A=\sin^{-1}\left(\frac{\sqrt{3}}{2}\right)=60^\circ[/tex]
II) To find BC, we will use the Law of Cosines. We do not know whether or not ΔABC is a right triangle, so we cannot use right triangle trigonometry or special right triangles.
The law of cosines is:
[tex]\displaystyle c^2=a^2+b^2-2ab\cos(C)[/tex]
Where a and b are side lengths and C is the angle between the side lengths. c is the side length opposite to the angle.
BC is opposite to A. Substitute:
[tex](BC)^2=(10\sqrt{3})^2+(6)^2-2(10\sqrt{3})(6)\cos(60^\circ)[/tex]
Simplify:
[tex]\displaystyle BC^2=336-120\sqrt{3}\left(\frac{1}{2}\right)=336-60\sqrt{3}[/tex]
Take the square root of both sides:
[tex]\displaystyle BC=\sqrt{336-60\sqrt{3}}\approx 15.23[/tex]
BC measures about 15.23 cm.
Notes:
In this case, the inverse sine of √3/2 will yield two answers: 60° and 120°. This is an example of an ambiguous case. Both of these angles will work. However, BC will be different. If ∠A is 60°, then BC is about 15.23. However, if ∠A is 120°, then BC is about 20.97. Both will result in the triangle having an area of 45 square cm, as well as AB measuring 10√3 and AC measuring 6.
Related Questions
A computer that originally cost $250 is on sale for 15%off. What is the sale
price of the computer?
Answers
Answer:
The computer costs $212.5
Step-by-step explanation:
First you multiply the original ammount by the percentage,or 15%,which is 0.15.Then you take that amount and subtract it from the original price.
[tex]250*0.15=37.5\\\\250-37.5=212.5[/tex]
The answer is $ 212.5 Dollars
Solve each of the following equations. Show its solution set on a number line. Check your answers |5x|=3
Answers
Answer:
|5x|=3
5x=3 or 5x=-3
divide both side by 5
x=3/5 or -3/5
here's the answer :))
answer answer answer
What’s the answer to this??
Answers
Answer:
arc Z = 100°
Step-by-step explanation:
arc Y = 80° x 2 = 160°
arc Z = (360° - 160°)/2 = 100° because the 2 chords are of equal length, then arc Z = the arc opposite Z
Henry had $22 and Ben had $17. Henry spent twice as much as Ben and was left with half as much as Ben. The amount of money that Ben spent is $____.
Answers
Answer:
Ben spent 9$
Step-by-step explanation:
Ben=x Henry=2x
17-x= 2(22-2x)
17-x=44-4x
-x+4x=44-17
3x=27
x=27/3
x=9 $ Ben spent
I need help with number 2
Answers
Answer:
I would help but the picture that's on this question isn't letting me see it so I'll just make a joke....... sorry
if you need help with #2 then you should probably go to a doctor
Solve for X. Enter the solutions from least to greatest.
(x – 7)^2-25 = 0
Answers
(x-7)^2=25
Take the square root from both sides
x-7=5
X= 12 .
Answer:
2,12
Step-by-step explanation:
khan
Please help
The function m is given in three equivalent forms.
Which form most quickly reveals the vertex?
Choose 1 answer:
m(x) = 2(x + 4)^2 – 8
m(x) = 2(x+6)(x + 2)
m(x) = 2x^2 + 16x + 24
Answers
At the deli counter, Marisol orders 740 grams of ham, 520 grams of turkey, and half as much roast beef as ham. What is the total mass in kilograms of Marisol's order?
Answers
Answer:
1.63 Kilograms
Step-by-step explanation:
I started by finding out what the roast beef weighed. Then I added 740, 520, and 370 (what the roast beef weighs). I can work that way because they are all in grams. The total off all that equals 1630 grams. Then I converted that to kilograms. Which will end up giving you 1.63 kilograms.
A group of nine friends go to a baseball game. Each friend buys either a hamburger or hot dog at the
game.
The group buys 6 hot dogs and 3 hamburgers for a total of $27.75.
• A hamburger costs $1.75 more than a hot dog.
What is the cost of a hamburger?
A
$2.50
B
$3.25
$3.75
$4.25
Answers
Answer:
$4.25
Step-by-step explanation:
27.75 - 5.25 = 22.5
22.5/9 = 2.5
2.5 + 1.75 = 4.25
1. (G. 12B) The radius of a circle is 5
inches. What is the length of a 70° arc?
(use 3.14 for 1)
Answers
Answer:
1.94 in
Step-by-step explanation:
The arc length formula is s = rФ. Here, r = 5 in and Ф = 70° But in this formula the central angle, Ф, must be in radians:
70°(1 rad)
-------------- = 0.389 rad
180°
Thus, the arc length here is s = (5 in)(0.889 rad) = 1.94 in
5, 5, 8, 8, 8, 9, 17, 19, 19, 19, 19, 22, 28
What is the median?
Answers
Answer:
17
Step-by-step explanation:
1. Arrange your number in numerical order
2. count how many numbers you have
3. if you have an odd number round divide by 2 and round up to gry the position of the median nunber.
4. if you have an even number divided by 2 go to the number in that position and average it with the number in the next higher position to get the median.
Can someone please help me with math.
Answers
Answer:
your answer is B for number one
Answer:
b, d, a
Step-by-step explanation:
A concrete mixing tub contains 34 liters of water and 22 liters of sand. Starting at the same time, water is added to the tub at a rate of 5 liters per minute,
while sand is also added to the tub at a rate of 7 liters per minute.
Part A
In how many minutes will the tub contain equal amounts of water and sand?
2 minutes
6 minutes
12 minutes
24 minutes
Answers
Answer:
6 minutes
6
6 minutes
6 minutes
If one of the angles in a triangle is 55 degrees then what are possible measurements of the other two angles?
Answers
Answer:
100° and 25°
Step-by-step explanation:
Total measure of the angles in a triangle is 180°
180 - 55 = 125
split 125° into 2
lots of possible answers
Will Give Brainliest!
f(1) = -3
f(n) = 2 * f(n-1) + 1
f(2) = ?
Answers
Answer:
f(1) = -3 f(n) = 2 f(n - 1) + 1 f(2)
Alternate form:
{f(n) = -f(1)/3, f(n - 1) = f(1)/2 - f(2)/2}
Answer:
f = -3
Step-by-step explanation:
F(1)=-3
Re-order the terms so constants are on the left
f . 1 = -3
1 f = -3
multiply by 1
1 f = -3
f = -3
The following table shows how much Dave gave each of his kids for allowance last month Find the median allowance
Answers
Answer:
7
Step-by-step explanation:
1. arrange the numbers from smallest to biggest
2. cross on each side until you reach a middle number
3. if there's two digits , add them both and divide by two
Answer:
7
Step-by-step explanation:
For each of the fractions below find fractions with denominators power of 10 getting closer and closer to it hence write it decimal form:
a) 1/4
b)1/3
c)23/11
Answers
Answer:
a) 1/4 = 0.25
b) 1/3 ≈ 0.333
c) 23/11 ≈ 2.090
Step-by-step explanation:
To find the fractions with denominators of powers of 10 that correspond to the given fractions, we express each fraction in their decimal form as follows;
a) 1/4 = 1/10×(10/4) = 1/10 × (2 + 2/4)
1/4 - 2/10 = 2/40 = 1/20
1/4 = 1/100 × (100/4) = 1/100 × 25
1/4 = 25/100 = 0.25
Therefore;
1/4 = 25/10² = 0.25
b) 1/3
1/3 = 1/10 × (10/3)
1/3 = 1/10 × (3 + 1/3)
1/3 - 3/10 = 1/30
The 3/10 with a denominator of 10 is closer to 1/3
Similarly, we get;
1/3 = 1/100 × (100/3) = 1/100 × (33 + 1/3)
1/3 - 33/100 = 1/300
The fraction 33/100 with a denominator of 100 is closer to 1/3
We can also get 1/3 - 333/1000 = 1/3000
Therefore; 1/3 ≈ 333/1000 = 0.333
c) 23/11
23/11 = 1/10 × (230/11) = 1/10 × (20 + 10/11)
23/11 - 20/10 = 10/110
23/11 = 1/100 × (2300/11) = 1/100 × (209 + 10/11)
23/11 - 209/100 = 10/1100 = 1/110
23/11 = 1/1000 × (23000/11) = 1/1000 × (2090 + 10/11)
23/11 - 2090/1000 = 10/11000 = 1/1100
Therefore;
23/11 ≈ 2,090/1,000 = 2.09
what expression is a factor of 18x²-15x+2
Answers
Answer:
Your answer is (6x−1)(3x−2)
Step-by-step explanation:
Julie has picked 10× 3 silver three red three green and one orange she now has a 12% chance of picking which color
Answers
Answer:
None of the colors
Step-by-step explanation:
The given parameters can be represented as:
[tex]Silver = 3[/tex]
[tex]Red = 3[/tex]
[tex]Green = 3[/tex]
[tex]Orange =1[/tex]
[tex]Total = 10[/tex]
Required
Which has a probability of 12%
To do this, we calculate the probability of each color.
This is calculated as:
[tex]P(Color) = \frac{Color}{Total}[/tex]
So, we have:
[tex]P(Silver) = \frac{Silver}{Total}[/tex]
[tex]P(Silver) = \frac{3}{10}[/tex]
Express as percentage
[tex]P(Silver) = 30\%[/tex]
[tex]P(Red) =\frac{Red}{Total}[/tex]
[tex]P(Red) =\frac{3}{10}[/tex]
Express as percentage
[tex]P(Red) =30\%[/tex]
[tex]P(Green) = \frac{Green}{Total}[/tex]
[tex]P(Green) = \frac{3}{10}[/tex]
Express as percentage
[tex]P(Green) = 30\%[/tex]
[tex]P(Orange) = \frac{1}{10}[/tex]
[tex]P(Orange) = 0.1[/tex]
Express as percentage
[tex]P(Orange) = 10\%[/tex]
So, we have:
[tex]P(Silver) = 30\%[/tex]
[tex]P(Red) =30\%[/tex]
[tex]P(Green) = 30\%[/tex]
[tex]P(Orange) = 10\%[/tex]
From the above calculations, none of the colors have a probability of 12%.
A school group is raising money for a trip. The group needs $450 for travel and $325 for food. They have 6 weeks to raise money selling $1 candy bars.
What is the least number of candy bars the group needs to sell each week to afford the trip?
Answers
Answer:
Step-In total, the amount of money they will need to raise is:
= 450 + 325
= $775
by-step explanation:
They have 6 weeks to raise this money so the amount they have to raise per week is at least:
= 775/6
= $130
The candy bars cost $1 each. They will therefore have to sell a minimum of 130 candy bars each week to afford the trip.
pls help will mark brainliest
Answers
Answer:
$3720
Step-by-step explanation:
If he makes $40 an hour for 60 hours, he makes $2400 there on the spot.
He worked 11 hours overtime, but it is double time, so 22 hours, and also, one and a half overtime pay, So, 22 hours × 40 × 1.5 = 22×60=1320. So, he made $1320 for working overtime.
In total, he made a total of 1320+2400=3720.
He made $3720.
If (3,2) —> (2, -3) represents a counter clockwise rotation of the point on a coordinate plane, how many degrees is the rotation?
A. 90°
B. 180°
C. 270°
D. 360°
Answers
A simple random sample from a population with a normal distribution of 103 body temperatures has x = 98.30°F and s = 0.61°F. Construct a 95% confidence interval estimate of the standard deviation of body temperature of all healthy humans.
Answers
Answer:
(98.2884 ; 98.3116)
Step-by-step explanation:
Given :
x = 98.30°F and s = 0.61°F
Sample size. n = 103
Zcritical at 95% = 1.96
Using the confidence interval relation :
x ± margin of error
Margin of Error :
Zcritical * s/√n
1.96 * 0.61/√103 = 0.0116
Lower boundary = (98.30 - 0.0116) = 98.2884
Upper boundary = (98.30 + 0.0116) = 98.3116
(98.2884 ; 98.3116)
Set of average city temperatures in April are normally distributed with a mean of 19.7°C and a standard deviation of 2°C. The average temperature of Cairo is 21.4°C. What proportion of average city temperatures are the higher than that of Cairo?
Answers
Answer:
The answer is "19.77%"
Step-by-step explanation:
Given:
[tex]\mu = 19.7\\\\ \sigma = 2\\\\\to P(x >21.4 ) = 1 - P(x< 21.4)\\\\[/tex]
[tex]= 1 - [\frac{P(x -\mu)}{ \sigma }< \frac{(21.4-19.7)}{2}]\\\\= 1 - P(z < 0.85)\\\\= 1 - 0.8023\\\\=0.1977\\\\=19.77\%[/tex]
What is p(x)???????????????
Answers
The area of a rectangular bathroom mirror is 10 square feet. The perimeter is 14 feet. What are the dimensions of the mirror?
Answers
Answer:
5 by 2
Step-by-step explanation:
It makes sense because:
Area: 5x2= 10 square feet
Perimeter: 5+5+2+2= 14 feet
1
Ms. K. has $63 in her bank account. A store credit her account with a $15 refund. How much does she now have
in the bank?
Answers
Answer:
48
Step-by-step explanation:
PLSS HELP THE TEACHER IS ASKING FOR MY ANSWERS CUZ I WAS SUPPOSED TO DO IT AND I NEVER WAS PREPARED PLSSS HELP IM NEXT PLS DRAW IT FOR MEE :( EVEN IF ITS EDITED I WOULD APPRECIATE TYSM HAVE A GOOD DAY!
Answers
Answer: what?
Step-by-step explanation:
I don’t know
Answer:
Just multiple each fraction by 2 on the denominator and numerator.
For the drawing part, all you have to do is draw lines until you get the number of the denominator.
Step-by-step explanation:
For. Example, 2/4 times 2 equals 4/8
So for this u would draw lines till you count that there are 8 lines.
I hope this helped you.
Have a nice day.
1 + 7^2
Ima be asking more questions be ready my amigos
Answers
Answer:
50
Step-by-step explanation:
Decimal Form:
0.02040816
Hope this helped, and please mark as Brainliest <3
The diagonal of a square is x units. What is the area of the square in terms of x?
o 1/2x^2 square units
O x^2 square units
2x square units
1/2x square units
Answers
Answer:
1/2(x²) square units
Step-by-step explanation
From the question,
Area of a Square(A) = L²
A = L²................. Equation 1
Where L = Lenght of the square
If the diagonal of the square is x,
Using pythagoras theorem,
a² = b²+c².................. Equation 2
Wherer a = x, b = c= L
Therefore,
x² = L²+L²
x² = 2L²
L² = x²/2
L = √(x²/2)
Substitute the value of L into equation 1
A = [√(x²/2)]²
A = x²/2 square unit.
A = 1/2(x²) square unit.
The right option is 1/2(x²) square units
