Question

A radio tower has a 64 ft Shadow cast by the sun. If the angle from the tip of the shadow to the top of the tower is 78.5°. what is the height of the tower?

Answer 1

Step-by-step explanation:

right-angled triangle, and law of sine (for any type of triangles) :

a/sin(A) = b/sin(B) = c/sin(C)

where the sides and the correlated angles are always opposite from each other.

and we know that the sum of all angles in a triangle is always 180°.

so, the angle at the foot of the radio tower is 90°.

the angle from the top of the shadow to the top of the tower is 78.5°.

so, the third angle (at the top of the tower) is

180 - 90 - 78.5 = 11.5°

and with the law of sine we get

height/sin(78.5) = 64/sin(11.5)

height = 64×sin(78.5)/sin(11.5) = 314.57005... ft