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 how far above the ground is the top of the slide, we can use trigonometry.
We know that the slide is 4.1 m long and makes an angle of 40° with the ground. We can use the sine of this angle to find the height.
sin(40°) = opposite/hypotenuse
Let's call the height we want to find "h". The opposite side is the height, and the hypotenuse is the length of the slide, 4.1m.
sin(40°) = h/4.1
To solve for "h", we can multiply both sides of the equation by 4.1:
4.1 * sin(40°) = h
Using a calculator to find the sine of 40°:
4.1 * 0.643 = h
h ≈ 2.64
The top of the slide is approximately 2.64 meters above the ground.