A loading ramp is 35 feet long and forms an angle measuring 10° with the ground. How high is the top end of the ramp off the ground? Round your answer to the nearest tenth?
make a sketch to see that
sin10° = height/35
height = 35sin10
= appr 6.1 ft
To find the height (h) of the top end of the ramp off the ground, we can use trigonometry.
In this case, we can use the tangent function, which is defined as the opposite side divided by the adjacent side. The opposite side is the height we want to find, and the adjacent side is the length of the ramp.
The formula for tangent is:
tan(angle) = opposite/adjacent
Rearranging the formula, we have:
opposite = tan(angle) * adjacent
Given that the length of the ramp (adjacent) is 35 feet and the angle is 10°, we can substitute these values into the formula:
opposite = tan(10°) * 35
To find the value of tangent of 10°, we can use a scientific calculator or an online trigonometry calculator. Plugging this into a calculator, we get:
opposite = 0.1763269807 * 35
Solving this, we find:
opposite ≈ 6.175 feet
So, the top end of the ramp is approximately 6.175 feet off the ground.