Question

jim is designing a seesaw for a childrens park. the seesaw should make an angle of 30° with the ground, and the maximum height to which it should rise is 2 meters, as shown below. what is the maximum length of the seesaw? 3 meters 3.5 meter 4 meters 4.5 meters

Explanation:

Step1: Identify the trig - relation

We know that in a right - triangle formed by the seesaw, the height it rises and the ground, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 30^{\circ}$ and the opposite side to the angle $\theta$ is the height the seesaw rises ($h = 2$ meters), and the hypotenuse is the length of the seesaw ($l$).
So, $\sin30^{\circ}=\frac{2}{l}$.

Step2: Solve for the length of the seesaw

Since $\sin30^{\circ}=\frac{1}{2}$, we have the equation $\frac{1}{2}=\frac{2}{l}$.
Cross - multiplying gives us $l\times1 = 2\times2$.
So, $l = 4$ meters.

Answer:

4 meters