The height of a loading platform is 4 feet. Determin the length of the ramp if it makes a 32 degree angle with the ground.
To determine the length of the ramp, we can use trigonometry. The 32-degree angle formed by the ramp and the ground is known as the angle of elevation.
In this case, the opposite side of the angle is the height of the loading platform, which is 4 feet. The adjacent side is the length of the ramp, which we need to find.
To find the length of the ramp, we can use the trigonometric function tangent (tan):
tan(angle) = opposite / adjacent
Plugging in the given values:
tan(32 degrees) = 4 / adjacent
To isolate the adjacent side, we can rearrange the formula:
adjacent = opposite / tan(angle)
Now we can substitute the values and solve for the adjacent:
adjacent = 4 / tan(32 degrees)
Using a scientific calculator or an online calculator, we can find the value of tan(32 degrees) is approximately 0.6249.
adjacent = 4 / 0.6249
Therefore, the length of the ramp is approximately 6.4 feet (rounded to one decimal place).
make a sketch , hypotenuse = ?
height = 4
use sin 32° = 4/h
h = 4/sin 32°
= .....