Question

An aerial photograph from a U-2 spy plane is taken of a building suspected of housing nuclear warheads. When the photograph is taken, the angle of elevation of the sun is 30∘. By comparing the shadow cast by the building in question to the shadows of other objects of known size in the photograph, scientists determine that the shadow of the building in question is 98 feet long.How tall is the bulding? (Round your answer to two decimal places.)

Answer 1

Answer:

Building is 56.58 feet long.

Step-by-step explanation:

Consider the provided information.

An aerial photograph from a U-2 spy plane is taken of a building suspected of housing nuclear warheads.

When the photograph is taken, the angle of elevation of the sun is 30°.

By comparing the shadow cast by the building in question to the shadows of other objects of known size in the photograph, scientists determine that the shadow of the building in question is 98 feet long.

As we know: $\tan\theta=\frac{opp}{adj}$

The value of tan 30 degrees is $\frac{1}{\sqrt{3} }$

$\tan30=\frac{h}{98}$

$\frac{1}{\sqrt{3}}=\frac{h}{98}$

$h=\frac{98}{\sqrt{3}}$

$h=56.58$

Hence, Building is 56.58 feet long.