Respuesta :
Let H = height of the lighthouse
5.5/2.2 = H/48
5/2 = H/48
H = 5*48/2 = 120 feet
5.5/2.2 = H/48
5/2 = H/48
H = 5*48/2 = 120 feet
Answer: The height of the lighthouse= 120 feet.
Step-by-step 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,
[tex]\frac{\text{height of lighthouse}}{\text{length of shadow cast by lighthouse}}=\frac{\text{height of friend}}{\text{length of shadow cast by friend}}[/tex]
[tex]\\\Rightarrow\frac{\text{height of lighthouse}}{48}=\frac{5.5}{2.2}\\\Rightarrow\text{height of lighthouse}=\frac{5.5}{2.2}\times48\\\Rightarrow\ \text{height of lighthouse}=5\times24=120\ feet[/tex]