Question

Steve wants to find the height of a radio tower in his neighborhood. He places a mirror on the ground 30 feet from the tower and walks backwards 3 feet until he can see the top of the tower in the mirror. Steve is 5 ft 6 in tall. How tall is the radio tower in feet? ​

Answer 1

Answer:

55 ft

Step-by-step explanation:

1ft = 12in → 6in = 0.5ft → 5ft 6in = 5.5ft

Look at the picture.

We know: the angle of incidence is equal to the angle of reflection (α).

We have two similar right triangles (AA). Therefore the corresponding sides are in proportion:

$\dfrac{h}{5.5}=\dfrac{30}{3}$

$\dfrac{h}{5.5}=10$             multiply both sides by 5.5

$h=55$