Question

Timelimit: 15 minutes. 11:08 remaining, x A radio tower is located 250 feet from a building. From a window in the building, a person determines that the angle of elevation to the top of the tower is 38 and that the angle of depression to the bottom of the tower is 27. How tall is the tower? Preview feet Points possible: 1 This is attempt 1 of 1. Submit

Answer 1

The height of tower is 322.7 feet.

Explanation:

Given

Distance between a building and tower= 250 feet

BCDE is a rectangle .Therefore, we have BC=ED and CD=BE=250 feet

In triangle ABE

`tan\theta=(perpendicula \; side )/(hypotenuse)`

`\theta=38^(\circ)`

`tan38^(\circ)=(AB)/(BE)`

`(AB)/(250)=0.781`

`AB=0.781*250`

AB=195.25 feet

In triangle EDC

`\theta=27^(\circ)`

`tan27^(\circ)=(ED)/(CD)`

`(ED)/(250)=0.509`

`ED=250*0.509`

ED=127.25 feet

ED=BC=127.25 feet

The height of tower=AB+BC

The height of tower=195.25+127.25=322.5 feet