Question

5.2 part 2
score: 0/10 answered: 0/10
question 1
a road up a hill makes an angle of 5.3° with the horizontal. if the road from the bottom of the hill to the top of the hill is 2.2 miles long, how high is the hill? round to at at least least 2 decimal places.
mi
question help: video ebook message instructor

Explanation:

Step1: Identify the trigonometric relationship

We can use the sine function. In a right - triangle (where the road is the hypotenuse, the height of the hill is the opposite side to the given angle), the formula is \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Let \(h\) be the height of the hill, \(\theta = 5.3^{\circ}\), and the hypotenuse \(c = 2.2\) miles. So, \(\sin(5.3^{\circ})=\frac{h}{2.2}\).

Step2: Solve for \(h\)

We can rewrite the equation as \(h = 2.2\times\sin(5.3^{\circ})\).
We know that \(\sin(5.3^{\circ})\approx0.0924\) (using a calculator in degree mode).
Then \(h=2.2\times0.0924 = 0.20328\)

Answer:

\(0.20\) mi