Question

Cassey uses a wheelchair and wants to get to the top of the stage shown in the picture. The stage is 2 meters off the ground. She has the option of using two ramps. Ramp X is 7 meters long and ramp Y is 3 meters long.

Answer 1

To calculate which ramp Cassey should use, we need to determine the angle of inclination for each ramp. This will tell us which ramp will require less effort for Cassey to ascend.

For Ramp X:
tan θ = opposite / adjacent
tan θ = 2 / 7
θ = tan⁻¹(2/7)
θ = 16.26°

For Ramp Y:
tan θ = opposite / adjacent
tan θ = 2 / 3
θ = tan⁻¹(2/3)
θ = 33.69°

From these calculations, we can see that Ramp X has a lower angle of inclination than Ramp Y. This means that it will be easier for Cassey to ascend the stage using Ramp X. Therefore, she should use Ramp X, which is 7 meters long.