Question

1
two wheelchair ramps, each 10 feet long, lead to the two ends of the entrance porch of mr. bells restaurant. the two ends of the porch are at the same height from the ground, and the start of each ramp is the same distance from the base of the porch. the angle of the first ramp to the ground is 24°.
which statement must be true about the angle of the second ramp to the ground?
a. nothing is known about the angle of the second ramp.
b. it could have any angle greater than or equal to 24°.
c. it could have any angle less than or equal to 24°.
d. it must have an angle of exactly 24°.

Explanation:

Step1: Define the ramp triangle

Each ramp forms a right triangle: hypotenuse (ramp length) = 10 ft, opposite side = porch height $h$, angle with ground = $\theta$. Use $\sin\theta=\frac{h}{10}$.

Step2: Analyze first ramp's height

For first ramp, $\theta=24^\circ$, so $h = 10\sin(24^\circ)$.

Step3: Compare second ramp's angle

Second ramp has same $h$ and same 10 ft length. Thus $\sin\theta_2=\frac{h}{10}=\sin(24^\circ)$. For $0^\circ<\theta<90^\circ$, sine is one-to-one, so $\theta_2=24^\circ$.

Answer:

D. It must have an angle of exactly 24°.