Question

use the following information to answer the next question. the ramp below has a rise of 3.2 and a run of 5.8. 12 a) calculate the angle of elevation of the ramp to one decimal place. show your work. b) calculate the percent grade of the ramp to one decimal place. show your work.

Explanation:

Step1: Recall tangent - angle relationship

In a right - triangle, $\tan(A)=\frac{\text{rise}}{\text{run}}$. Here, $\text{rise} = 3.2$ and $\text{run}=5.8$, so $\tan(A)=\frac{3.2}{5.8}$.

Step2: Calculate the angle of elevation

$A=\arctan(\frac{3.2}{5.8})$. Using a calculator, $A=\arctan(0.551724)\approx 29.2^{\circ}$ (rounded to one decimal place).

Step3: Recall percent - grade formula

The percent grade of a ramp is given by $\text{Percent Grade}=\frac{\text{rise}}{\text{run}}\times 100\%$.

Step4: Calculate the percent grade

Substitute $\text{rise} = 3.2$ and $\text{run}=5.8$ into the formula: $\text{Percent Grade}=\frac{3.2}{5.8}\times 100\%$. $\frac{3.2}{5.8}\times 100\%\approx0.551724\times 100\% = 55.2\%$ (rounded to one decimal place).

Answer:

a) 29.2°
b) 55.2%