Question

You know the bed of the truck is at a height of 1.00 m and you need a ramp that makes an angle of 40 ∘ with the ground if you are to be able to push the couch. Use the sine function to determine how long of a board you need to use to make a ramp that just reaches the 1.00- m high truck bed at a 40 ∘ angle to the ground.

Answer 1

To determine the length of the board needed to make a ramp that reaches the 1.00 m high truck bed at a 40° angle to the ground, use the sine function.

Step-by-step explanation:

To determine the length of the board needed to make a ramp that reaches the 1.00 m high truck bed at a 40° angle to the ground, we can use the sine function. The sine of an angle is equal to the ratio of the length of the opposite side to the hypotenuse. In this case, the opposite side is the height of the truck bed, which is 1.00 m. So, we have:

sin(40°) = 1.00 m / x

To find x, we can rearrange the equation:

x = 1.00 m / sin(40°)

Using a calculator, we can calculate that x is approximately 1.5355 m. Therefore, you will need a board that is at least 1.54 m long to make a ramp that reaches the 1.00 m high truck bed at a 40° angle to the ground.