Question

A wooden ramp is to be built with one end on the ground and the other end at the top of a short staircase. If the top of the staircase is 6 ft from the ground and the angle between the ground and the ramp is to be 26, how long does the ramp need to be?

Round your answer to four decimal places.

Answer 1

To find the length of the ramp, we can use the concept of trigonometry. Using the tangent function and the given angle and height, we can find the length of the ramp to be approximately 13.0542 ft.

Step-by-step explanation:

To find the length of the ramp, we can use the concept of trigonometry. Since we know the height of the staircase is 6 ft and the angle between the ground and the ramp is 26 degrees, we can use the tangent function to find the length of the ramp. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.

Using the tangent function, we can set up the equation:

tan(26) = opposite/adjacent

tan(26) = 6/adjacent

Now, we can solve for the adjacent side, which represents the length of the ramp:

adjacent = 6/tan(26)

Calculating this value gives us approximately 13.0542 ft. Rounded to four decimal places, the length of the ramp should be approximately 13.0542 ft.