Question

1. a step has a height of 6 inches. a ramp starts 5 feet away from the base of the step, making a 5.7° angle with the ground. what can you say about the angle the ramp would make with the ground if the ramp starts closer to the step?

a. the angle would decrease.
b. the angle would increase.
c. the angle would stay the same.
d. we cannot determine anything about the angle.

Explanation:

We can model this as a right triangle where the height of the step (6 inches, a fixed opposite side to the ramp angle) is constant. The horizontal distance from the step base is the adjacent side. When the ramp starts closer, the adjacent side length decreases. Using the tangent function $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$, if the adjacent side gets smaller while the opposite side stays the same, $\tan(\theta)$ increases, so the angle $\theta$ increases.

Answer:

B. The angle would increase.