Question

A cell phone tower in a field casts a shadow of 100 ft. At the same time, a 4 ft 6 in post near the tower casts a shadow of 3 ft 4 in. Find the height of the tower in feet. (Hint: make a drawing)

Answer 1

This is the concept of linear proportionality;
We are required to find the height of the tower in feet. The height of the tower will be found as follows;
[height of tower]/[length of the shadow of tower]=[height of post]/[length of shadow of the post]
height of the tower =h
height of the shadow=100ft
height of post=4 ft 6in=4 1/2 ft= 9/2 ft
length of the post's shadow=3 ft 4 in 3 1/3 ft=10/3 ft

N/B 1 ft= 12 inches

thus;
h/100=(9/2)/(10/3)
multiplying both sides by 100 we get:
h=(9/2)/(10/3)*100
h=9/2*3/10*100
h=135 ft

the answer is 135 ft