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