Question

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 elevation is 33º. Find the height of the
building?​

Answer 1

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