In △ABC, AB = 13.2m, BC = 6.9m and ∠ACB = 90°. H lies on AC such that ∠BHC = 46°. Find (i) ∠ABH (ii) The length of AH

Answers

Answer 1

Answer:

(i) ∠ABH = 14.46⁰

(ii) The length of AH = 4.6 m

Step-by-step explanation:

From the image uploaded;

Consider △ABC;

the length of b is calculated by applying Pythagoras theorem as follows;

b² = c² - a²

b² = (13.2)² - (6.9)²

b² = 126.63

b = √126.63

b = 11.25 m

Also, ∠ABC is calculated as;

[tex]Cos \ B = \frac{a^2+c^2-b^2}{2ac} \\\\Cos \ B = \frac{(6.9)^2+(13.2)^2-(11.25)^2}{2(6.9 \times13.2)}\\\\ Cos \ B = \frac{95.288}{182.16} \\\\ Cos \ B = 0.5219 \\\\B = Cos ^{-1} (0.5231)\\\\B = 58.46 ^o[/tex]

Consider △CBH, ∠CBH is calculated as;

∠CBH = 90⁰ - 46⁰ = 44⁰

(i) ∠ABH will be calculated as;

∠ABH = θ

θ + 44⁰ = ∠ABC

θ + 44⁰ = 58.46⁰

θ = 58.46⁰  - 44⁰

θ = 14.46⁰

Thus, ∠ABH = 14.46⁰

(ii) The length of AH

length HC is calculated as;

[tex]tan \ 46^o =\frac{6.9}{HC} \\\\HC = \frac{6.9}{tan \ 46^o } \\\\HC = 6.66 \ m[/tex]

length of AH = CA - HC

x = b - HC

x = 11.25 - 6.66

x = 4.6 m

length of AH = 4.6 m

In ABC, AB = 13.2m, BC = 6.9m And ACB = 90. H Lies On AC Such That BHC = 46. Find (i) ABH (ii) The Length

Related Questions

50 Points. what is the value of x

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Answer:

X will be = to 6°

Cause the lengths is 6

so 6 ×6° = 36°

I hope am wrong

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Step-by-step explanation:

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A factory worker can package 180 games in 15 minutes. How many games can he package per minute?

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Will Give Brainly if correct
Select all the angle measurements that are correct
g=24,
h=24,
f=151,
g=29,
b=132,
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Answers

Answer:

a = 132

b = 132

d = 29

e = 29

f = 151

g = 24

h = 24

Jane had 3/4 of a pound of blueberries. Jane let her friend Jack eat 1/2 of the blueberries. How many pounds of blueberries did Jack eat?

Answers

Answer:

Jack eat 3/8 pounds of the blueberries.

Step-by-step explanation:

Jane had 3/4 of a pound of blueberries.

Jack eat 1/2 of the blueberries.

How many pounds of blueberries did Jack eat?

= 1/2 of 3/4 pounds of blueberries

= 1/2 × 3/4

= (1*3) / (2*4)

= 3/8 pounds

Jack eat 3/8 pounds of the blueberries.

How much would a 20% tip be

Answers

Answer: 1.18 OR 0.18

Step-by-step explanation:

Answer:

It would depend of what your bill is.

Step-by-step explanation:

Here is how to find the tip of a bill.

Move the decimal, then double the number.

Move the decimal point in your pretax bill one place to the left to get $5.375 from $53.75.

Round up to the next easy number: $5.40.

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find the values of x in [0,360) which satisfy 2cot^2x=-3cscx

Answers

Answer:

The values of x is -30 degrees and undefined

None of these values fall within the given range

Thus, no value within the given range is the solution to the equation

Step-by-step explanation:

Here, we want to find the value of x that works for the equation in the selected range

2cot^2x = -3csc x

Mathematically, from trigonometry;

cot^2x = csc^2x - 1

Substitute this above

2(csc^2x - 1)= -3csc x

let csc x = b

2(b^2-1) = -3b

2b^2 - 2 + 3b = 0

2b^2 + 3b - 2 = 0

2b^2 + 4b - b - 2 = 0

2b(b+ 2) - 1( b + 2) = 0

(2b-1)(b + 2) = 0

2b = 1

b = -2

b = 1/2 = 0.5

or b = -2

Recall;

csc x = b

x = csc^-1 b

x = csc^-1 0.5

x = undefined

Secondly;

b = -2

x = csc^-1 (-2)

x = -30 degrees

As we can see , between the points

0 ≤ x < 360

None of our answers fall in these range

What does this symbol ± mean?

Answers

Plus or Minus.

For example.

5 ± 2 = 5 + 2 or 5-2

Therefore the answer is 7 or 3.

Answer:

It means that the number can be positive or negative.

Step-by-step explanation:

I hope this helps!!!

FIRST ONE GETS BRAINLEYST FREE IF CORRECT!!


Which of these statements uses transitional words to connect ideas?
A. Many states have more than one national park. Florida has the Everglades and the Dry Tortugas.
B. Arizona has a very famous national park. It is called the Grand Canyon. It is famous and draws visitors from all over the world.
C. The beautiful, lush Hawaiian islands are the home of two of the world’s most active volcanoes.
D. South Dakota's Badlands are home to a lot of wildlife, including bison, bighorn sheep, and swift foxes.

Answers

Answer:

D

Step-by-step explanation:

I had this on my quiz and said it was right. Hope this helps!

In ΔBCD, \text{m}\angle B = (4x-14)^{\circ}m∠B=(4x−14) ∘ , \text{m}\angle C = (x-1)^{\circ}m∠C=(x−1) ∘ , and \text{m}\angle D = (6x+8)^{\circ}m∠D=(6x+8) ∘ . What is the value of x?X?

Answers

Answer:

x = 17

Step-by-step explanation:

The sum of angle in the triangle BCD is 180 degrees

Given;

<B = 4x  -14

<C = x - 1

<D = 6x + 8

Required

Find x

Since <B + <C + <D = 180, hence;

4x - 14 + x - 1 + 6x + 8 = 180

11x -7 = 180

11x = 180+7

11x = 187

x = 187/11

x = 17

Hence the value of x is 17

Are the triangles congruent? and why?
SSS
SAS
ASA
AAS
HL

Answers

Answer:

they are congruent because SAS

Step-by-step explanation:

What is true about the relationship between miles and gallons?

Answers

D.,,,,,,,,,,,,,,,,,,,,

Valentina bought 12 puzzles each with the same number of pieces. The total amount of pieces is 19,200. How many pieces are in each puzzle box?

Answers

Answer: 1600

Step-by-step explanation:

If there is a total amount of 19200 pieces within 12 puzzle boxes, then we'll have to divide 19200 by 12.

19200 ÷ 12 = 1600.

In conclusion, 1600 pieces are in each puzzle box.

Hope this helps!

Answer:

1,600 pieces per puzzle

Step-by-step explanation:

19,200/12= 1,600

you divide because you have the total amount of puzzle pieces and you have the amount of puzzles so

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Answers

Step-by-step explanation:

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Therefore y = x and line B depicts that.

Answer:

B)

Step-by-step explanation:

It's B) because if you look at the slope of the line it goes through all the boxes points.

Another way to do it is take to points and do

m=y2-y1/x2-x1

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Answers

The answers are

25 envelopes per minute
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27 miles per gallon

Answer:

1. 25 envelopes

2. 82 words per minute

3. 27 Miles per gallon

Step-by-step explanation:

Evaluate 1.3 x 0.03​

Answers

Answer:

0.039

Step-by-step explanation:

Multiply.

1.3 x 0.03 = 0.039

Answer:
0.039
Explanation:
1.3x0.03=0.039

* The nth term of sequence A is 3n − 2 The nth term of sequence B is 10 − 2n Sally says there is only one number that is in both sequence A and sequence B. Is Sally right? You must explain your answer.

Answers

Answer:

Sally is not right

Step-by-step explanation:

Given the two sequences which have their respective [tex]n^{th}[/tex] terms as following:

Sequence A. [tex]3n - 2[/tex]

Sequence B. [tex]10 - 2n[/tex]

As per Sally, there exists only one number which is in both the sequences.

To find:

Whether Sally is correct or not.

Solution:

For Sally to be correct, we need to put the [tex]n^{th}[/tex] terms of the respective sequences as equal and let us verify that.

[tex]3n-2=10-2n\\\Rightarrow 3n+2n=10+2\\\Rightarrow 5n=12\\\Rightarrow n = \dfrac{12}{5}[/tex]

When we talk about [tex]n^{th}[/tex] terms, [tex]n[/tex] here is a whole number not a fractional number.

But as per the statement as stated by Sally [tex]n[/tex] is a fractional number, only then the two sequences can have a number which is in the both sequences.

Therefore, no number can be in both the sequences A and B.

Hence, Sally is not right.

If the measurment of the angles of a triangle are 3b,2b,and 4b then what is the smallest angle

Answers

Given:

The measurement of the angles of a triangle are 3b,2b,and 4b.

To find:

The smallest angle.

Solution:

According to the angle sum property, the sum of all angles of a triangle is 180 degrees.

[tex]3b+2b+4b=180^{\circ}[/tex]           [Angle sum property]

[tex]9b=180^{\circ}[/tex]

Divide both sides by 9.

[tex]b=20^{\circ}[/tex]

Now,

[tex]3b=3(20^{\circ})=60^{\circ}[/tex]

[tex]2b=2(20^{\circ})=40^{\circ}[/tex]

[tex]3b=4(20^{\circ})=80^{\circ}[/tex]

Therefore, the smallest angle is 40 degrees.

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Answers

(4y+4)+(3x-3)=180 (cause they are supplementary)

4y+3x=179
4y=179-3x
so
y= 179/4 - 3/4x (write these as a fraction; the x goes to the whole fraction)

u cant get a more exact result with 2 unknowns:)

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Answers

Answer:

it's almost $100 and there's $17 off. so 99.99-17  would make the exact cost 82.99

82.99/99.99= 0.8299 so you payed 83% and that would make it so you got a 17% discount.

but if you didn't want to do all the math, you could've just rounded the 99.99 up to 100, and $17 would make it a 17% discount.

A furniture salesman earns 7% commission for his sales.
How much commission would he earn, if he sold a couch for
$800?

Answers

He would earn $56


Hope this helps :))

Answer:

He would get 56 dollars.

Step-by-step explanation:

56$

Question 5. Solve x + 9 = -13

Answers

Answer:

x = -22

Step-by-step explanation:

x + 9 = -13

  -9     -9

x = -13 - 9

x = -22

Move all terms not containing x to the right side of the equation.

Answer: x = -22

coach purchased footballs and basketballs from two different stores.
Each football costs the same amount, and each basketball costs the same
amount.
At the first store, the coach paid $110 for 5 footballs and 14 basketballs.
At the second store, the coach paid $82.50 for 10 footballs and 6
basketballs.
What was the cost in dollars of each basketball?

Answers

Answer:

$6.25

Step-by-step explanation:

Let football cost be f and basketball cost be b

We have two equations as per given:

5f + 14b = 11010f + 6b = 82.50

We need to find b, therefore we'll eliminate f

To do so we'll double the first equation and subtract the second one:

2(5f + 14b) - (10f + 6b) = 2(110) - 82.5028b - 6b = 220 - 82.5022b = 137.5b = 137.5/22b = 6.25

Each basketball costs $6.25

Question:

Coach purchased footballs and basketballs from two different stores.

Each football costs the same amount, and each basketball costs the same amount.

At the first store, the coach paid $110 for 5 footballs and 14 basketballs.

At the second store, the coach paid $82.50 for 10 footballs and 6 basketballs.

What was the cost in dollars of Each basketball?

Answer:

Probably 7


REAL Answer:
6.25

Your Welcome! (^·^)

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WHAT IS X???
1.2/0.96 = 3.0/x

Answers

Answer:

x= 2.4

Step-by-step explanation:

Answer:

2.4 or 12/5

Step-by-step explanation:

1.2/0.96=3/x

convert the decimal into a fraction---- 6/5 /0.96= 3/x

Simplify the complex fraction-----5/4 = 3/x

simplify the equation using cross-mulitpication----- 5 x = 12

divide both sides of the equation by 5--- x= 12/5

Check if the solution is in the defined range

Alternitive form:

x=2 2/5, x =2.4

In Louisville, 40% of the population is female and 60% are males. 36% of Louisville's population is under 18. The ratio of males to females who are under 18 is 2:1. If there are 1,176 males who are under 18, what is the population of females who are over 18.

Answers

Answer:

1411 females

Step-by-step explanation:

Given that:

Male population = 60%

Female population = 40%

36% of total population are under 18

Ratio of male to female under 18 = 2 : 1

Males under 18 = 1176

Females over 18 =?

The population of females under 18:

If males under 18 = 1176

Then female under 18 = 1176 / 2 = 588

Hence number of population under 18 = (1176 + 588) = 1764

1764 = 36% of the entire population

Hence, (100 - 36)% = 64% of the entire population are over 18

1764 = 0.36

x = 0.72

x = (0.72 * 1764) / 0.36

x = 3528

Hence, 40% of the population above 18 are female

0.4 * 3528 = 1411.2

= 1411 females are over 18

solve the inequality −8 ≤ z + 6.4

Answers

Answer:

-14.4<or=z

Step-by-step explanation:

-8-6.4or = z+6.4-6.4

-14.4_<z

2,995,384 - 89 = blank​

Answers

Answer:

hope this helps

Step-by-step explanation:

2,995,384 - 89

==2,995,295

Answer:

the answer is 2,995,295

Please someone help me with this

Answers

Answer:

Looks like at (3,21) the graph intersects, meaning both values are equal to one another.

Given the figure below, find the values of x and z.
(10x - 65)
(9x - 49)

Answers

(10x - 65) degrees is equal to (9x - 49) degrees, therefore you can set them into an equation.

(10x - 65) = (9x - 49)

By subtracting 9x in both sides,

(10x - 9x) - 65 = (9x -9x) - 49

x - 65 = -49

By adding 65 in both sides,


x - 65 + 65= -49 + 65
x = 16


Next, to find the value of z, it’s important to know that the straight line has 180 degrees. Then you would substitute the x value you found into one of your equation and subtract it from 180.

10 (16) - 65 = 160 - 65 = 95

Now you know that (10x - 65) degrees is equal to 95 degrees,

180 - 95 = z = 85


Answer: x = 16
z = 85
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