Question

jim is designing a seesaw for a children’s park. the seesaw should make an angle of 30° with the ground, and the maximum height to which it should rise is 1 meter, as shown below. what is the maximum length of the seesaw? 1.4 meters 2 meters 0.5 meters 1 meter

Explanation:

Step1: Identify the trigonometric relationship

We have a right triangle where the height (opposite side to the 30° angle) is 1 meter, and the length of the seesaw is the hypotenuse. We use the sine function: $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$.

Step2: Substitute values and solve for hypotenuse

Given $\theta = 30^\circ$ and opposite side = 1 meter. So $\sin(30^\circ) = \frac{1}{\text{hypotenuse}}$. Since $\sin(30^\circ) = \frac{1}{2}$, we have $\frac{1}{2} = \frac{1}{\text{hypotenuse}}$. Solving for hypotenuse (length of seesaw), we get $\text{hypotenuse} = \frac{1}{\sin(30^\circ)} = \frac{1}{\frac{1}{2}} = 2$ meters.

Answer:

2 meters (corresponding to the option "2 meters")