Question

An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 29 feet up. The ladder makes an angle of 71∘

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

Answer 1

30.7

Step-by-step explanation:

sin 71° = 29/ ladder length

so length = 29/ sin 71° = 30.7

Answer 2

Using the sine function, the length of the ladder which makes a 71° angle with the ground and reaches 29 feet up can be found to be approximately 30.7 feet when rounded to the nearest tenth.

Step-by-step explanation:

To find the length of the ladder in the given scenario, we can use trigonometry since we have an angle and the opposite side of a right triangle. Specifically, we can use the sine function, which relates the opposite side of a triangle to its hypotenuse when the angle is known. The formula to use is:

sin(angle) = opposite side / hypotenuse

Plugging in the values from the question:

sin(71°) = 29 / hypotenuse

To solve for the hypotenuse (length of the ladder), we rearrange the formula:

hypotenuse = 29 / sin(71°)

Carrying out the calculation gives us the length of the ladder:

hypotenuse ≈ 29 / 0.9455 ≈ 30.7 feet

Therefore, the length of the ladder, rounded to the nearest tenth, is approximately 30.7 feet.