Question

question 5
1 pts
a 5 - foot woman casts a 1.2 - foot shadow while a lighthouse casts
a 48 - foot shadow. how tall is the lighthouse?
200 ft
180 ft
195 ft
210 ft
question 6
1 pts
two triangles are similar. the ratio of their corresponding sides
is \\( \frac { 3 } { 5 } \\). if the shorter triangles perimeter is 24, find the perimeter
of the larger triangle.

Explanation:

Step1: Set up proportion

Let the height of the lighthouse be \(h\). Since the triangles (formed by the woman and her shadow, and the lighthouse and its shadow) are similar, the ratios of corresponding sides are equal. So \(\frac{\text{Woman's height}}{\text{Woman's shadow}}=\frac{\text{Lighthouse height}}{\text{Lighthouse shadow}}\), which is \(\frac{5}{1.2}=\frac{h}{48}\).

Step2: Solve for \(h\)

Cross - multiply: \(1.2h = 5\times48\). Then \(1.2h=240\). Divide both sides by \(1.2\): \(h=\frac{240}{1.2}=200\).

Answer:

A. 200 ft