Question

A tourist looks out from the observation deck of the Space Needle in Seattle. The deck is at a height of 520 ft. She sees her friend on the ground below at an angle of depression of 80.2 What is the distance between the two? Round your answer to the nearest tenth of a foot.

Answer 1

Last option 527.7 ft

Explanation:

From the diagram attached we can see the angle of depression is 80.2 which is equal to ∠ACB (alternate angles)

Height of the deck AB = 520 ft. and we have to calculate the distance H between the tourist and her friend.

Sin ∠ACB =
`(AB)/(AC)`

Now we apply sin rule sin 80.2 =
`(520)/(H)`

`.9854=(520)/(H)`

`H = (520)/(.9854) = 570 ft`

So the tourist and her friend are 527.7 ft apart.