A 55 foot tall radio tower r feet from an observer subtends an angle of 3°.

Question

A 55 foot tall radio tower r feet from an observer subtends an angle of 3°.

 

Use the arc length formula to estimate r(the distance between the observer and the radio tower) to the nearest foot.

 

r≈    feet

 

Answer 1

I'm using trig.

a=55

b=r

α=3°

a/sinα=b/sinβ=c/sinγ

55/.052335=1050.902=c; if this is a right triangle. Also β=87°. sin90°=1.

r/.9986=1050.902

r=1049.462..........ft.

Answer 2

Draw and label a diagram.

tan 3° = 55 / r

r tan 3 ° = 55

r = 55 / tan 3°