Question

As shown in the diagram below, a building casts a72-foot shadow on the ground when the angle ofelevation of the Sun is 40°.588BEBB140°-72 ftHow tall is the building, to the nearest foot?

Answer 1

EXPLANATION

Shadow=72 foot

The tall can be obtained by pplying the Pythagorean Theorem as shown as follows:

$\tan \theta=\frac{Opposite\text{ Cathethus}}{\text{Adjacent cathetus}}$

As we can see, theta = 40 degrees, Opposite= unknown, Adjacent=72 ft

Replacing terms:

$\tan 40=\frac{\text{unknown }}{72}$

Multiplying both sides by 72:

$72\cdot\tan 40=unknown$

Solving the trig.:

$72\cdot0.84=\text{unknown}$

Multiplying numbers:

$60.48\text{ = unknown}$

Switching sides:

$\text{unknown = 60.48}$

Answer: the building is 60 feet tall