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.
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.