Question

1. a) indoor ramps have a steepness of 1 cm of rise for every 9 cm of run. for an indoor ramp to rise 90 cm, how far along the ground should it run? b) what is the angle of elevation of the ramp? express your answer to the nearest degree.

Explanation:

Step1: Set up proportion for part a

Let $x$ be the run - distance. The ratio of rise to run is constant. We have the proportion $\frac{1}{9}=\frac{90}{x}$.

Step2: Solve the proportion for $x$

Cross - multiply: $1\times x = 9\times90$. So, $x = 810$ cm.

Step3: Calculate the angle of elevation for part b

We know that the slope (steepness) is $\tan\theta=\frac{\text{rise}}{\text{run}}$. Here, $\tan\theta=\frac{1}{9}$.

Step4: Find the angle $\theta$

$\theta=\arctan(\frac{1}{9})$. Using a calculator, $\theta\approx 6^{\circ}$ (rounded to the nearest degree).

Answer:

a) 810 cm
b) $6^{\circ}$