Answer
The grade of the hill is 3:7 or 3 to 7.
Work Step by Step
1. Find the $\angle B$ in $\triangle ABC $
$\angle B = 180 - (90 + 23)$ (Angles in a triangle add to 180˚)
$\angle B = 180 - 113$
$\angle B = 67˚$
$\angle A = 23˚$ (Given)
$\angle C = 90˚$ (Given)
2. Use the sine law to find the value of b
$\frac{b}{sin67} = \frac{3}{sin23}$
$b = \frac{3sin67}{sin23}$
$b = \frac{2.6715...}{0.39073...}$
$b = \frac{2.6715...}{0.39073...}$
$ b = 7.067 ft$
$b \approx7$ ft
3. Take the a and b value to find the grade
Grade $ = a$ to $b$
Grade $= 3 $ ft to $7$ ft
