Question

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

Using complete sentences, explain how the scientist can use only these two measurements to calculate the distance between the Earth and the Sun.
A. Trigonometric ratios
B. Pythagorean theorem
C. Law of cosines
D. Distance formula

Answer 1

The scientist can use the Pythagorean theorem to calculate the distance between the Earth and the Sun using the right triangle formed by the shooting star, Earth, and the Sun. The hypotenuse of the triangle represents the distance between the Earth and the Sun.

Step-by-step explanation:

The scientist can use the Pythagorean theorem to calculate the distance between the Earth and the Sun using the right triangle formed by the shooting star, Earth, and the Sun. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the distance between the Earth and the Sun is the hypotenuse, and the measurements of the shooting star and Earth represent the other two sides.

For example, if the shooting star is 10 units away from the Earth, and the Earth is 1 unit away from the Sun, then the distance between the Earth and the Sun can be calculated as follows:

a² + b² = c²
1² + 10² = c²
1 + 100 = c²
101 = c²
c ≈ 10.05 units

Therefore, the distance between the Earth and the Sun is approximately 10.05 units.