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

Answer:

Length of wire = 50 ft

Step-by-step 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

$sin C = \frac{AB}{AC}$

we can plug AB= 45, ∠C= 64°and AC=x

so we have

$sin(64)$°$=\frac{45}{x}$

$xsin(64)$°$=45$

$x=\frac{45}{sin(64)}$

now we have sin 64°=0.8988

$x=\frac{45}{0.8988}$

$x=50.07$ ft

rounding to nearest foot

x= 50 ft