How to do i solve it

A man finds that the angle of elevationof a building is 22º. After walking 20 m towards the building, he finds that the angle of

tensa zangetsu [6.8K]

Answer:

The height of the building is 21.38 m

Step-by-step explanation:

Trigonometric Ratios

The ratios of the sides of a right triangle are called trigonometric ratios.

The image attached shows the measures and angles provided in the problem. The first angle of elevation is y=22°, the man walks B=20 m and finds the new angle of elevation is x=33°.

It's required to find the height of the building H.

The tangent ratio relates the opposite side with the adjacent side of a given angle. Applying it to the larger triangle:

$\displaystyle \tan y=\frac{\text{opposite leg}}{\text{adjacent leg}}$

$\displaystyle \tan 22^\circ=\frac{H}{D+B}$

Multiplying by D+B:

$\tan 22^\circ(D+B)=H$

Dividing by tan 22°

$\displaystyle D+B=\frac{H}{\tan 22^\circ}$

Subtracting B:

$\displaystyle D=\frac{H}{\tan 22^\circ}-B\qquad\qquad[1]$

Applying to the smaller triangle:

$\displaystyle \tan 33^\circ=\frac{H}{D}$

Multiplying by D:

$\tan 33^\circ D=H$

Substituting from [1]:

$\displaystyle \tan 33^\circ \left(\frac{H}{\tan 22^\circ}-B\right)=H$

Substituting values:

$\displaystyle 0.6494 \left(\frac{H}{0.4040}-20\right)=H$

Operating:

$1.6074H-12.988=H$

$1.6074H-H=12.988$

$0.6074H=12.988$

$H = 12.988/0.6074$

H = 21.38 m

The height of the building is 21.38 m

3 0

3 years ago

A 12 oz bottle of a new soda costs $2.49. What is the unit rate, rounded to the nearest tenth of a cent?

OlgaM077 [116]

The answer is .21 !!!!!

6 0

4 years ago

SOMEONE HELP ME PLEASEEE

nadya68 [22]

Answer:

A) X≥4

B) Can't see question

C)x<8

D) x>40

E)x≥5

F) Can't see question

G)x ≥43

H) x ≤75

Step-by-step explanation:

4 0

2 years ago

Whats the quotient of simplest from for 5 wholes divide by 2\9 ?

posledela

Keep Change Flip!!!
Keep: the first fraction 5 or 5/1
Change: Division sign to multiplication sign
Flip (reciprocal): the second fraction
So you get 5/1*9/2= 45/2 which simplified to 22 1/2

7 0

3 years ago

Another math problem I cant solve.

Mamont248 [21]

Answer: x = 7, y = -3

Step-by-step explanation:

3y = 26 - 5x --> added 5x to both sides to get: 5x + 3y = 26

Elimination method (I am going to eliminate "x":

5x + 3y = 26 → 6(5x + 3y = 26) → 30x + 18y = 156

6x + 7y = 21 → -5(6x + 7y = 21) → -30x - 35y = -105

-17y = 51

÷-17 ÷-17

y = -3

Now, input y = -3 into one of the original equations to solve for "x":

3y = 26 - 5x

3(-3) = 26 - 5x

-9 = 26 - 5x

-9 -26 = -5x

-35 = -5x

7 = x

7 0

4 years ago