Question

a water slide is a straight ramp 25 m long that starts from the top of a tower. if the angle the slide forms with the top of the tower is 33°, determine the height of the tower. round your answer to the nearest meter.
a. 30 m
c. 24 m
b. 25 m
d. 21 m
please select the best answer from the choices provided
o a
o b
o c
o d

Explanation:

Step1: Identify trigonometric relation

We have a right - triangle where the length of the hypotenuse (the water - slide) is $l = 25$ m and the angle between the slide and the top of the tower is $\theta=33^{\circ}$. We want to find the height $h$ of the tower. We use the sine function since $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\sin\theta=\sin(33^{\circ})$ and the hypotenuse is 25 m, and the height of the tower is the side opposite to the given angle. So, $\sin(33^{\circ})=\frac{h}{25}$.

Step2: Solve for height

We can rewrite the equation as $h = 25\times\sin(33^{\circ})$. We know that $\sin(33^{\circ})\approx0.5446$. Then $h = 25\times0.5446=13.615$ m. This is incorrect as we mis - interpreted the angle. If the angle between the slide and the top of the tower is $33^{\circ}$, then the angle between the slide and the vertical (which we should use in the right - triangle formed by the tower, the ground, and the slide) is $90^{\circ}-33^{\circ} = 57^{\circ}$. Now, using $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, where the adjacent side to the $57^{\circ}$ angle is the height of the tower $h$ and the hypotenuse is 25 m. So, $h = 25\times\cos(33^{\circ})$. Since $\cos(33^{\circ})\approx0.8387$, then $h=25\times0.8387 = 20.9675\approx21$ m.

Answer:

D. 21 m