The bottom of the ladder on a horizontal flat surface rests against a wall. It makes an angle of elevation of 35°. The bottom of the ladder is 42 ft from the base of the wall. How long is the ladder? Round your answer to the nearest whole number.
42/x = cos35°
To find the length of the ladder, we can use trigonometry. In this case, we have the angle of elevation and the distance between the bottom of the ladder and the base of the wall.
1. Draw a diagram:
Start by drawing a horizontal line to represent the ground, and a vertical line to represent the wall. Then, draw a slanted line to represent the ladder. Label the angle of elevation as 35° and the distance between the bottom of the ladder and the base of the wall as 42 ft.
2. Use trigonometry:
We can apply the trigonometric function for the tangent of an angle to find the length of the ladder. The tangent function relates the ratio of the opposite side to the adjacent side of a right triangle.
tan(angle) = opposite / adjacent
In this case, the opposite side is the height of the wall (the length of the ladder) and the adjacent side is the distance between the bottom of the ladder and the base of the wall. So, we have:
tan(35°) = height / 42
3. Solve for the height:
Plug in the values into the equation:
tan(35°) = height / 42
To solve for the height, multiply both sides of the equation by 42:
height = 42 * tan(35°)
Using a calculator, find the value of tan(35°):
height ≈ 42 * 0.7002
height ≈ 29.4072 ft
4. Round the answer:
Since the question asks for the length of the ladder rounded to the nearest whole number, we round the calculated height to the nearest whole number.
The length of the ladder is approximately 29 ft.