Question

Avery leans a 24-foot ladder against a wall so that it forms an angle of 80° with the

ground. How high up the wall does the ladder reach? Round your answer to the
nearest tenth of a foot if necessary.

Answer 1

Using trigonometry and the cosine function, a 24-foot ladder leaning at an 80° angle with the ground reaches approximately 4.2 feet up the wall.

Step-by-step explanation:

To determine how high up the wall a 24-foot ladder reaches when it is leaning against the wall at an 80° angle with the ground, we can use trigonometry. Specifically, we will use the cosine function, which relates the adjacent side of a right triangle (the height the ladder reaches up the wall) to the hypotenuse (the length of the ladder).

The cosine of an angle in a right triangle is equal to the length of the adjacent side divided by the length of the hypotenuse. So we can set up the equation as follows:

• cos(80°) = height / 24

To find the height, we rearrange the equation:

• height = 24 × cos(80°)

Then we use a calculator to find the cosine of 80 degrees and multiply by 24:

height ≈ 24 × 0.1736 ≈ 4.1664 feet

Rounding to the nearest tenth of a foot gives us: height ≈ 4.2 feet

Therefore, the ladder reaches approximately 4.2 feet up the wall.

Answer 2

Answer:23.6ft

Step-by-step explanation:

SOHCAHTOA

sin(80)=(o/24)

Multiply both sides by 24 and 24 on the right side will cancel out.

24sin(80)=23.6ft