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

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 $\tan 11^{\circ}= \frac{Perpendicular}{Base}$

$\tan 11^{\circ}= \frac{BC}{AB}$

$\tan 11^{\circ}= \frac{x}{1}$

$0.194= \frac{x}{1}$

x = 0.194 mile

Since 1 mile =5280 feet

So, x = $0.194 \times 5280$

= 1024.32 feet.

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

Answer 2

1250 feet hoped i helped