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. We will use the sine function, which is defined as the opposite side divided by the hypotenuse.
Given that the length of the slide is 4.1 m and the angle it makes with the ground is 40°, we can assign the opposite side (height of the slide) as h and the hypotenuse (length of the slide) as 4.1.
Using the sine function, we have:
sin(40°) = h / 4.1
Rearranging the equation to solve for h, we have:
h = 4.1 * sin(40°)
Calculating this expression, we find:
h ≈ 4.1 * 0.6428 ≈ 2.63848
Therefore, to the nearest hundredth of a meter, the top of the slide is approximately 2.64 meters above the ground.