Question

Sally, Max, and William are on a camping trip in the forest. They are riding their bikes through the forest and come across a clearing. In the clearing, there are several trees and a small plane. Sally is curious about the physics of the plane, so she asks Max and William to help her measure the distance from the plane to the nearest tree. They use a measuring tape to find that the distance is 60 meters. They also measure the height of the plane to be 10 meters and the height of the tree to be 20 meters. Using the principles of physics, they calculate the angle at which the plane is flying relative to the tree. What is the angle?

Answer 1

Answer: The angle at which the plane is flying relative to the tree is 19.47 degrees.

Step-by-step explanation:

To calculate the angle at which the plane is flying relative to the tree, we can use the principle of trigonometry and the Pythagorean theorem. Since we know the distance from the plane to the nearest tree (60 meters), the height of the plane (10 meters), and the height of the tree (20 meters), we can use these measurements to form a right triangle with the plane, the tree, and the ground.

Using the Pythagorean theorem, we can calculate the length of the hypotenuse of the right triangle. The length of the hypotenuse is the distance between the plane and the top of the tree. The hypotenuse is calculated by the square root of (distance^2 + height of the plane^2 + height of the tree^2)

The angle we are trying to calculate is opposite to the height of the tree, therefore we can use the tangent function:

tan(angle) = opposite/adjacent

opposite = height of the tree = 20m

adjacent = distance = 60m

angle = arctan(20/60) = arctan(1/3) = 19.47122063449069 degrees

The angle at which the plane is flying relative to the tree is 19.47 degrees.