Question

A wire is attached to the top of a 45-foot telephone pole and anchored to the ground. The angle of elevation is 64 degrees. How long is the wire to the nearest foot?

Answer 1

Length of wire = 50 ft

Explanation:

In the figure below AB is the telephone pole and C is the point on the ground where wire is anchored.

so we have

AB= 45 ft

∠ACB= 64°

Let is assume the length of the wire be x ft

now in Δ ABC

`sin C = (AB)/(AC)`

we can plug AB= 45, ∠C= 64°and AC=x

so we have

`sin(64)`°
`=(45)/(x)`

`xsin(64)`°
`=45`

`x=(45)/(sin(64))`

now we have sin 64°=0.8988

`x=(45)/(0.8988)`

`x=50.07` ft

rounding to nearest foot

x= 50 ft