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Nady [450]
3 years ago
8

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?​
Mathematics
1 answer:
tensa zangetsu [6.8K]3 years ago
3 0

Answer:

<em>The height of the building is 21.38 m</em>

Step-by-step explanation:

<u>Trigonometric Ratios</u>

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

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