Question

The lighthouse on the beach casts a shadow that is 48 feet long. Your friend is 5.5 feet tall and casts a shadow that is 2.2 feet long. What is the height of the lighthouse?

Answer 1

Let H = height of the lighthouse
5.5/2.2 = H/48
5/2 = H/48
H = 5*48/2 = 120 feet

Answer 2

Answer: The height of the lighthouse= 120 feet.

Explanation:

Let the shadow cast by lighthouse on the beach and the friend occur on the same time, then the triangle formed by lighthouse and its shadow and the triangle formed by friend and its shadow must be similar.

We know that the sides of two similar triangles are proportional.

Therefore,

`\frac{\text{height of lighthouse}}{\text{length of shadow cast by lighthouse}}=\frac{\text{height of friend}}{\text{length of shadow cast by friend}}`

`\\\Rightarrow\frac{\text{height of lighthouse}}{48}=(5.5)/(2.2)\\\Rightarrow\text{height of lighthouse}=(5.5)/(2.2)*48\\\Rightarrow\ \text{height of lighthouse}=5*24=120\ feet`