Question

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

Answer 1

SOLUTIONS

Explanation:

Let's assume that the right triangle formed is like the one shown in the figure attached, where "d" represents the distance between the Earth and the Sun.

Then:

The scientist can use only these two measurements to calculate the distance between the Earth and the Sun by applying one of the trigonometric functions: Tangent of an angle.

The scientist can substitute these measurements into tan Ф = opp/adj , and solve for the distance "d".

Knowing that:

Ф = x⁰

opposite = y

adjacent = d

Then:

tanФ = y/d

And solving for "d":

`d=(y)/(tanx^0)`

Answer:

- The scientist can use these two measurements to calculate the distance between the Earth and the Sun by applying one of the trigonometric functions: Tangent of an angle.

The scientist can substitute these measurements into and solve for the distance between the Earth and the Sun.

`d=(y)/(tanx^0)`