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:
[tex]\displaystyle \tan y=\frac{\text{opposite leg}}{\text{adjacent leg}}[/tex]
[tex]\displaystyle \tan 22^\circ=\frac{H}{D+B}[/tex]
Multiplying by D+B:
[tex]\tan 22^\circ(D+B)=H[/tex]
Dividing by tan 22°
[tex]\displaystyle D+B=\frac{H}{\tan 22^\circ}[/tex]
Subtracting B:
[tex]\displaystyle D=\frac{H}{\tan 22^\circ}-B\qquad\qquad[1][/tex]
Applying to the smaller triangle:
[tex]\displaystyle \tan 33^\circ=\frac{H}{D}[/tex]
Multiplying by D:
[tex]\tan 33^\circ D=H[/tex]
Substituting from [1]:
[tex]\displaystyle \tan 33^\circ \left(\frac{H}{\tan 22^\circ}-B\right)=H[/tex]
Substituting values:
[tex]\displaystyle 0.6494 \left(\frac{H}{0.4040}-20\right)=H[/tex]
Operating:
[tex]1.6074H-12.988=H[/tex]
[tex]1.6074H-H=12.988[/tex]
[tex]0.6074H=12.988[/tex]
[tex]H = 12.988/0.6074[/tex]
H = 21.38 m
The height of the building is 21.38 m
