Question

A pole that is 3.1 m tall casts a shadow that is 1.57 m long. At the same time, a nearby tower casts a shadow that id 50.5 m long. How tall is the tower? Round your answer to the nearest meter.​

Answer 1

Step-by-step explanation:

an object and its shadow create a right-angled triangle.

2 objects and their shadows at the same time create therefore two similar right-angled triangular

triangles.

that means the angles are the same, and each side length of one triangle correlates to the corresponding side length of the other triangle by the same factor.

so, when we know the factor of one pair of sides, we can calculate the lengths of the others by using the same factor.

therefore,

1.57 × f = 50.5

f = 50.5 / 1.57 = 32.1656051...

the height of the tower is then

3.1 × f = 3.1 × 32.1656051... = 99.7133758... m ≈ 100 m