galileo wanted to release a wooden ball and an iron ball from a height of 150 meters and measure the…

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

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

Answer

Answer:

$579.56$

Explanation:

Step1: Identify the trig - relation

We know that $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 15^{\circ}$, the opposite side to the angle $\theta$ is the height $h = 150$ meters, and the hypotenuse $d$ is the distance Galileo walks up the inclined plane.

Step2: Solve for the hypotenuse

We have $\sin15^{\circ}=\frac{150}{d}$. Since $\sin15^{\circ}=\sin(45^{\circ}- 30^{\circ})=\sin45^{\circ}\cos30^{\circ}-\cos45^{\circ}\sin30^{\circ}=\frac{\sqrt{2}}{2}\times\frac{\sqrt{3}}{2}-\frac{\sqrt{2}}{2}\times\frac{1}{2}=\frac{\sqrt{6}-\sqrt{2}}{4}\approx0.2588$. Then $d=\frac{150}{\sin15^{\circ}}=\frac{150}{0.2588}\approx579.56$ meters.