Question

A road up a hill makes an angle of 14 degrees with the horizontal. If the road from the bottom of the hill to the top of the hill is 1.7 miles long, how high is the top of the hill?

Round to the nearest tenth of a mile.
Answer:miles

Answer 1

Answer: To find the height of the hill (the vertical distance from the bottom to the top), we can use trigonometry. The angle between the road and the horizontal is 14 degrees, and the length of the road (hypotenuse) is 1.7 miles.

Let's call the height of the hill "h" (in miles). The trigonometric relationship we'll use is:

sin(angle) = opposite / hypotenuse

In this case, the opposite side is the height "h," and the hypotenuse is 1.7 miles. Plugging in the values:

sin(14 degrees) = h / 1.7

Now, solve for "h":

h = sin(14 degrees) * 1.7

Using a calculator:

h ≈ 0.2512 * 1.7 ≈ 0.4275 miles

So, the height of the top of the hill is approximately 0.4 miles (rounded to the nearest tenth of a mile).