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 77degrees

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

Answer 1

The length of the ladder is 22.7 feet.

Step-by-step explanation:

To find the length of the ladder, we can use trigonometry. The ladder forms a right triangle with the ground and the wall. The angle between the ground and the ladder is 77°. We know the height of the wall is 22 feet, so we can use the sine function to find the length of the ladder.

Sin(77°) = opposite/hypotenuse

Sin(77°) = 22/x

Cross multiplying, we get:

x = 22/sin(77°)

Using a calculator, we find that the length of the ladder is approximately 22.7 feet. Rounding to the nearest tenth, the length of the ladder is 22.7 feet.