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 top of the slide above the ground, we can use trigonometry.
Let h be the height of the top of the slide above the ground.
We can create a right triangle with the slide as the hypotenuse, the height of the top of the slide as the opposite side, and the length of the slide on the ground as the adjacent side.
We know the length of the slide (opposite side) is 4.1 m, and the angle with the ground is 40 degrees.
We can use the sine function to relate the angle, the opposite side, and the hypotenuse:
sin(40°) = h/4.1
Solving for h:
h = 4.1 * sin(40°)
h ≈ 4.1 * 0.6428
h ≈ 2.63
Therefore, the height of the top of the slide above the ground is approximately 2.63 meters.