Question

practice quiz 3 - ratios, tangent ratio and angle of elevation

1. calculate the missing side using the pythagorean theorem
2. calculate the slope and angle of elevation
3. a wheelchair ramp is being built to rise to a landing that is 2400 cm above the ground. building regulations say that the ramp can have a maximum rise of 2.5 cm per 30 cm of run

a) what is the total run for the wheelchair ramp?
b) what is the angle of elevation?
learning goal 3: i can calculate sides using pythagorean theorem; i can use tangent ratio to find angles of elevation

Explanation:

Step1: Calculate total run for wheelchair ramp

Set up proportion. Let $x$ be total run. $\frac{2.5}{30}=\frac{2400}{x}$. Cross - multiply: $2.5x = 2400\times30$. Then $x=\frac{2400\times30}{2.5}=28800$ cm.

Step2: Calculate angle of elevation

The tangent of the angle of elevation $\theta$ is given by $\tan\theta=\frac{\text{rise}}{\text{run}}$. Here, $\tan\theta=\frac{2.5}{30}=\frac{1}{12}$. So, $\theta=\arctan(\frac{1}{12})\approx 4.76^{\circ}$

Answer:

a) 28800 cm
b) Approximately $4.76^{\circ}$