Question

An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 22 feet up. The ladder makes an angle of 66° with the ground.

Find the length of the ladder. Round your answer to the nearest tenth of a foot if necessary.

Answer 1

Approximately 51.1 feet.

Explanation:

The problem can be solved using trigonometry, specifically the cosine function. The cosine of an angle in a right triangle is defined as the adjacent side divided by the hypotenuse. In this case, the adjacent side is the height of the wall (22 feet) and the hypotenuse is the length of the ladder we’re trying to find.

So, we have:

cos(66°) = 22 / length_of_ladder

Rearranging the equation to solve for the length of the ladder gives us:

length_of_ladder = 22 / cos(66°)

length_of_ladder = 22 / cos(66°)

Calculating, we find that the length of the ladder is approximately 51.1 feet.