Question

The angle of elevation from the base to the top of a waterslide is given as:

a. 15 degrees

b. 17 degrees

c. 20 degrees

d. 25 degrees

The horizontal extension of the slide is:

a. 100 meters

b. 120 meters

c. 150 meters

d. 180 meters
To approximate the height (( h )) of the waterslide, you can use the:

a. Cosine of the angle of elevation

b. Sine of the angle of elevation

c. Tangent of the angle of elevation

d. Arcsine of the angle of elevation

The formula for calculating the height of the waterslide is:

a. h = 150 ×cos(17^°)

b. h = 150 ×sin(17^°)

c. h = 150 ×tan(17^°)

d. h = 150 ×arcsin(17^°)

Answer 1

The height of the waterslide can be calculated using the tangent of the angle of elevation. Since you are given the horizontal extension, you multiply this by the tangent of the angle to find the height h = 150 × tan(17°).

Step-by-step explanation:

To approximate the height (h) of the waterslide, you would use the sine of the angle of elevation. The sine function relates the opposite side of a right-angled triangle (in this case, the height of the waterslide) to the hypotenuse (the length of the slide). However, we are given the horizontal extension of the slide, not the hypotenuse. The horizontal extension is the adjacent side in this right-angled triangle. Therefore, we actually need to use the tangent of the angle of elevation, since the tangent function relates the opposite side to the adjacent side.

The correct formula for calculating the height of the waterslide, given the horizontal extension and the angle of elevation, is h = horizontal extension × tan(angle of elevation). Therefore, if the horizontal extension is 150 meters and the angle of elevation is 17 degrees, the correct formula to use would be h = 150 × tan(17°).