Question

galileo wanted to release a wooden ball and an iron ball from a height of 150 meters and measure the duration of their fall. he found a plane with an incline of 15° that he could climb until he gets to an altitude of 150 m. how far should galileo walk up the inclined plane? round your final answer to the nearest hundredth. meters

Explanation:

Step1: Identify the trigonometric relationship

We have a right triangle where the height (opposite side to the angle \(15^\circ\)) is 150 meters, and we need to find the length of the inclined plane (hypotenuse). The sine of an angle in a right triangle is defined as \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\). So, \(\sin(15^\circ)=\frac{150}{x}\), where \(x\) is the length of the inclined plane.

Step2: Solve for \(x\)

Rearranging the formula from Step 1, we get \(x = \frac{150}{\sin(15^\circ)}\). We know that \(\sin(15^\circ)\approx0.2588\). Plugging in the value, we have \(x=\frac{150}{0.2588}\approx579.62\).

Answer:

\(579.62\)