Question

John is looking up at the top of the Empire State Building from 1 mi. away and measures the angle of elevation to be 11 degrees. Use this information to find the approximate height of the Empire State Building to the nearest foot.

Answer 1

1250 feet hoped i helped

Answer 2

Refer to the attached image.

Let the height of the Empire State Building = BC = 'x'

John is standing at distance from Empire State Building = AB = 1 mile

The angle of elevation = 11°

In triangle ABC,

Consider
`\tan 11^(\circ)= (Perpendicular)/(Base)`

`\tan 11^(\circ)= (BC)/(AB)`

`\tan 11^(\circ)= (x)/(1)`

`0.194= (x)/(1)`

x = 0.194 mile

Since 1 mile =5280 feet

So, x =
`0.194 * 5280`

= 1024.32 feet.

So, the height of the Empire State Building is 1024.32 feet.