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.
579.62 meters

Explanation:

Step1: Identify the trigonometric relationship

We have a right triangle where the opposite side to the angle \(15^\circ\) is the altitude (150 m) and the hypotenuse is the distance along the inclined plane (\(d\)) we need to find. The sine function relates the opposite side and the hypotenuse: \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\)
So, \(\sin(15^\circ)=\frac{150}{d}\)

Step2: Solve for \(d\)

Rearrange the formula to solve for \(d\): \(d = \frac{150}{\sin(15^\circ)}\)
We know that \(\sin(15^\circ)\approx0.2588\) (using a calculator for the sine of \(15^\circ\))
Then \(d=\frac{150}{0.2588}\approx579.62\)

Answer:

\(579.62\) meters