Question

Dante is standing at horizontal ground level with the base of the Empire State Building in New York City. The angle formed by the ground and the line segment from his position to the top of the building is 48.4°. The height of the Empire State Building is 1,472 feet. Find his distance from the Empire State Building to the nearest foot.

A. 7.65 ft
B. 1, 968 ft
C. 1,307 ft
D. 2, 217 ft

Answer 1

The correct answer is option C.

Explanation:

Height of Empire State Building = 1,472 feet

Angle formed by the line segment from the point of ground on which Dante is positioned to the top of the building is 48.4°.

Distance of Dante from the Empire State Building =?

In the fig ,ΔABC

AB = 1,472 feet, BC = ? , θ= 48.4°

`\tan\theta =(Perpendicular)/(base)`

`\tan 48.4^o=(AB)/(BC)`

`BC=(AB)/(\tan 48.4^o)=(1,472 feet)/(1.1263)=1,306.9 feet\approx 1,307 feet`

Distance of Dante from the Empire State Building is 1,307 feet.

Answer 2

C. 1307 ft

Explanation:

Given:

Angle = 48.4 degrees

Height, opposite side= 1472 feet

his distance from the Empire State Building, base=x

Now as per the trigonometric ratios:

Tan∅= Opposite/base

tan(48.4)= 1472/x

x=1472/(1.13)

x=1302.65

his distance from the Empire State Building is 1302.65 feet!