Question

An electrical tower casts a 120-foot shadow. At the same time, a 10-foot

street sign casts a shadow of 8 feet. What is the height of the tower?

O A. 270 ft
O B. 150 ft
O C. 120 ft
O D. 180 ft

Answer 1

B. 150 feet.

Explanation:

The tower and the street sign and their shadows form 2 similar triangles.

So the corresponding lengths are in the same ratio, then:

120 / 8 = h / 10 where h is the height of the tower.

8h = 120 * 10

h = 120 * 10 / 8

= 150 feet.

Answer 2

Set up a ratio with the height over the shadow.

Let the height of the tower be X

The ratio of the tower is x/120

The ratio if the sign is 10/8

Set them to equal and solve for x:

x/120 = 10/8

Cross multiply:

8x = 1200

Divide both sides by 8:

x = 1200/8

x =150

The answer is B. 150 ft.