Question

1. jon is building a wheelchair ramp at his grandmothers house. the ramp will rise 1.2 m over a run of 7.2 m. jon will purchase roll roofing to lay on the ramp to create a non - slip surface.

a) what length of roll roofing will jon have to purchase to cover the wheelchair ramp?
b) what is the angle of elevation of the ramp?

Explanation:

Step1: Recall Pythagorean theorem for part a

For a right - triangle (ramp is a right - triangle with rise and run as legs), the length $l$ of the hypotenuse (ramp length) is given by $l=\sqrt{r^{2}+s^{2}}$, where $r = 1.2$ m (rise) and $s=7.2$ m (run).
$l=\sqrt{(1.2)^{2}+(7.2)^{2}}=\sqrt{1.44 + 51.84}=\sqrt{53.28}\approx7.3$ m

Step2: Recall tangent function for part b

The angle of elevation $\theta$ of the ramp can be found using the tangent function $\tan\theta=\frac{\text{rise}}{\text{run}}$. Here, $\tan\theta=\frac{1.2}{7.2}=\frac{1}{6}$. Then $\theta=\arctan(\frac{1}{6})\approx9.46^{\circ}$

Answer:

a) The length of the roll roofing (ramp length) is approximately $7.3$ m.
b) The angle of elevation of the ramp is approximately $9.46^{\circ}$