Question

An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 34 feet up. The ladder makes an angle of 63^{\circ}

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

Answer 1

Answer & Explanation:

To solve this problem, we can use the sine function to find the length of the ladder. The sine of an angle is defined as the ratio of the opposite side of the angle to the hypotenuse of a right triangle. In this case, the opposite side of the angle is the height of the electric box, which is 34 feet, and the hypotenuse is the length of the ladder.

We can set up the following equation to find the length of the ladder:

sin(63) = 34 / L

Where L is the length of the ladder. We can solve for L by rearranging the terms in the equation and using the sine function in a calculator:

L = 34 / sin(63)

The value of sin(63) is approximately 0.9128, so the length of the ladder is approximately 34 / 0.9128 = 37.14 feet. Rounding to the nearest tenth of a foot, the length of the ladder is 37.1 feet.