Step-by-step explanation:
right-angled triangle, the sum of all angles in a triangle is always 180°, the law of sine
a/sin(A) = b/sin(B) = c/sin(C)
with the sides and the correlated angles being opposite from each other.
the angle of elevation with the sun is 58°.
that means also the angle at the tip of the shadow up is 58°.
and because the angle at the foot of the tower is 90°, the third angle from the top of the tower down to the end of the shadow is
180 - 90 - 58 = 32°
so, for the law of sine we have
height/sin(58) = 50/sin(32)
height = 50×sin(58)/sin(32) = 80.01672645... ft
