Question

A ladder, with its foot in the street, makes an angle of 30 degrees with the street when its top rests on a building on one side of the street and makes an angle of 40 degrees with the street when its top rests on a building on the other side of the street. Then there is a 10 ft wide sidewalk on each side of the street. If the ladder is 50 ft long, how wide is the street?
52ft
72ft
62ft
42ft

Answer 1

the answer would be 82 ft

Answer 2

The width of the street according to the description in the task content is; 62 ft.

What is the width of the street?

First, we must determine the horizontal distance between the feet of the ladder and each of the houses which it leans on as follows;

For House A;

• Distance = 50Cos30 = 43.30 ft.

For House B;

• Distance = 50Cos40 = 38.30 ft

Ultimately, the width of the street is; 43.30 ft + 38.30 ft = 81.60 ft = 82 ft - 20 ft (from the 10ft sidewalk on each side) is; 62ft.

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