Layla leans a 26-foot ladder against a wall so that it forms an angle of 61^(@) with the ground. How high up the wall does the ladder reach? Round your answer to the nearest tenth of a foot if necessary.

Identify Relationship: Identify the relationship between the angle, the ladder, and the height reached on the wall. The ladder forms a right triangle with the wall and the ground. The height up the wall is the opposite side of the angle, the ladder is the hypotenuse, and the ground is the adjacent side. We will use the sine function to find the height.Use Sine Function: Use the sine function to calculate the height. The sine of an angle in a right triangle is equal to the opposite side divided by the hypotenuse. Therefore, sin(61°) = height / 26 feet.Calculate Sine: Calculate the sine of 61 degrees. Using a calculator, find sin(61°). Make sure the calculator is set to degrees.Multiply to Find Height: Multiply the sine of 61 degrees by the length of the ladder to find the height. height = sin(61°) * 26 feet.Perform Calculation: Perform the calculation. height = sin(61°) * 26 ≈ 0.8746 * 26 ≈ 22.7396 feet.Round to Nearest Tenth: Round the answer to the nearest tenth of a foot. The height up the wall the ladder reaches is approximately 22.7 feet.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Layla leans a $26$ -foot ladder against a wall so that it forms an angle of $61^{\circ}$ with the ground. How high up the wall does the ladder reach? Round your answer to the nearest tenth of a foot if necessary.

View step-by-step help

Full solution

Q. Layla leans a

26

-foot ladder against a wall so that it forms an angle of

61^{\circ}

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

Identify Relationship: Identify the relationship between the angle, the ladder, and the height reached on the wall. $\newline$ The ladder forms a right triangle with the wall and the ground. The height up the wall is the opposite side of the angle, the ladder is the hypotenuse, and the ground is the adjacent side. We will use the sine function to find the height.
Use Sine Function: Use the sine function to calculate the height. $\newline$ The sine of an angle in a right triangle is equal to the opposite side divided by the hypotenuse. Therefore, $\sin(61^\circ) = \frac{\text{height}}{26 \text{ feet}}$ .
Calculate Sine: Calculate the sine of $61$ degrees. $\newline$ Using a calculator, find $\sin(61^\circ)$ . Make sure the calculator is set to degrees.
Multiply to Find Height: Multiply the sine of $61$ degrees by the length of the ladder to find the height. $\newline$ $\text{height} = \sin(61^\circ) \times 26 \text{ feet}.$
Perform Calculation: Perform the calculation. $\newline$ $\text{height} = \sin(61°) \times 26 \approx 0.8746 \times 26 \approx 22.7396$ feet.
Round to Nearest Tenth: Round the answer to the nearest tenth of a foot. $\newline$ The height up the wall the ladder reaches is approximately $22.7$ feet.