A slide is 4.1 m long and makes an angle with the ground of 40°. To the nearest hundredth of a meter, how far above the ground is the top of the slide? Please show all work in order to receive full credit.

Answer 1

To find the height of the slide above the ground, we can use trigonometry. The height is the opposite side of the 40° angle, and the length of the slide (horizontal distance) is the adjacent side. We can use the tangent function to find the height.

Let h be the height of the slide.
We have the equation tan(40°) = h/4.1m.

To solve for h, we multiply both sides of the equation by 4.1m:
4.1m * tan(40°) = h.

Using a calculator, we find:
h ≈ 2.78m.

Therefore, the top of the slide is approximately 2.78 meters above the ground.