Victor drives 300 meters up a hill that makes an angle of 13° with the horizontal. To the nearest tenth of a meter, what horizontal distance has he covered?
A. 307.9 meters
B. 292.3 meters
C. 69.3 meters
D. 67.5 meters
The horizontal distance that Victor has covered is the adjacent side of the right triangle formed by the hill and the horizontal ground. We can use trigonometry to find this distance.
First, we need to find the length of the opposite side (the height that Victor has climbed). We can use the definition of sine:
sin(13°) = opposite/hypotenuse
sin(13°) = x/300
x = 300*sin(13°)
x ≈ 67.5 meters
Next, we can use the definition of cosine to find the length of the adjacent side (the horizontal distance):
cos(13°) = adjacent/hypotenuse
cos(13°) = d/300
We want to solve for d, so we can rearrange the equation:
d = 300*cos(13°)
Using a calculator, we get:
d ≈ 292.3 meters
So the answer is B. Victor has covered approximately 292.3 meters horizontally.