A hill rises from the horizontal at 15º. The road leading straight up the hill is 800 meters long. How much higher is the top of the hill than the base of the hill? Round to the nearest meter. (Enter only the number.)
As usual, draw a figure.
You have the hypotenuse, and the angle.
h/800 = sin 15º = .2588
h = 207m
To find out how much higher the top of the hill is than the base, we can use trigonometry. Specifically, we'll use the sine function.
First, let's define the known values:
- The length of the road leading straight up the hill is 800 meters.
- The angle at which the hill rises from the horizontal is 15 degrees.
We can now use the sine function to find the vertical component of the hill's rise.
sin(θ) = opposite/hypotenuse
In this case, the opposite side is the height we want to find, and the hypotenuse is the length of the road.
sin(15) = height/800
To solve for the height, we can rearrange the equation:
height = sin(15) * 800
Using a calculator, we find:
height ≈ 204.802
Therefore, the top of the hill is approximately 204.802 meters higher than the base of the hill. Rounded to the nearest meter, the answer is 205 meters.