A shooting star forms a right triangle with the Earth and the Sun, as shown below:

A right triangle is shown with the vertices labeled Earth, Sun, and Shooting Star. The angle formed by the Sun is labeled x degrees and the side between the Earth and the Sun is labeled y.

A scientist measures the angle x and the distance y between the Earth and the Sun. Using complete sentences, explain how the scientist can use only these two measurements to calculate the distance between the Earth and the shooting star.

Question

Mathematics

Heidi Wilcox

2 July, 09:40

A shooting star forms a right triangle with the Earth and the Sun, as shown below:

A right triangle is shown with the vertices labeled Earth, Sun, and Shooting Star. The angle formed by the Sun is labeled x degrees and the side between the Earth and the Sun is labeled y.

A scientist measures the angle x and the distance y between the Earth and the Sun. Using complete sentences, explain how the scientist can use only these two measurements to calculate the distance between the Earth and the shooting star.

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Answers (1)

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Carolyn Caldwell · Answer 1

If the right angle is the angle made by the sides Earth-Sun and Earth-Shooting Star, then the scientist need only the given two measurements to calculate the distance between the Earth and the shooting star by using the trigonometric function tangent.

Since tangent is the ratio between the length of the opposite side and the adjacent side, we have:

tan x = y / Earth-ShootingStar

Earth-ShootingStar = y / tan x

Since both y and x are given, the distance between Earth and the Shooting Star can be calculated.