Given:
The length of the building's shadow is 136 feet
Angle of elevation is 64 degrees
We have to find the height of the building.
Now, the building's shadow is given that means it is the base length from the
angle of elevation to the building.
That is,
Now, we apply trigonometric ratio:
[tex]\text{tan 64}^{\circ}=\frac{perpendicular}{\text{base}}[/tex][tex]\tan \text{ 64=}\frac{perpendicular}{136}[/tex]
Now,
[tex]\begin{gathered} \text{perpendicular}=136\times\tan \text{ 64} \\ =136\times2.05 \\ =278.8\text{ ft} \end{gathered}[/tex]
Hence, the height of the building is 279 ft.
