Question

Kyle bought a ticket to see his favorite basketball team playing at home. His seat is in the terrace section, about 198 feet from the center of the court. If the angle of depression to the court is 57 degrees, which of the following represents the height Kyle is sitting?

Answer 1

Kyle is sitting at a height of 166.07

Answer 2

The height at which Kyle is sitting is 166.04 feet from the ground

Explanation:

Let the height of the Kyle's seat be h.

Distance from center to the seat of Kyle = 198 feet

Consider Figure ABC

Angle of depression = 57°

Angle
`\alpha` = 57° (alternative interior angles )

`\sin\alpha =(BC)/(AB)`

`\sin 57^o=0.8386=(h)/(198 feet)`

`h=198 feet* 0.8386=166.04 feet`

The height at which Kyle is sitting is 166.04 feet from the ground