Kai loves to hike. He wants to hike up a trail that rises at an angle of 40°. The vertical distance from the top of the trail to the bottom is 120 m. How far would he walk up the trail?

Answer 1

To find how far Kai would walk up the trail, we can use trigonometry. The vertical distance represents the height of the triangle, the distance Kai walks represents the hypotenuse of the triangle, and the angle of 40° is opposite the height.

We can use the trigonometric ratio tangent to find the distance Kai would walk:
tan(40°) = height / distance walked

Rearranging the equation to solve for distance walked:
distance walked = height / tan(40°)
distance walked = 120 m / tan(40°)
distance walked ≈ 150.40 m

Therefore, Kai would walk approximately 150.40 meters up the trail.