Question

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

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 Sun and the shooting star.

Answer 1

The positions of the sun, earth and shooting star form a right angled triangle, where distance between earth and sun is 'y', and the angle 'x°' is given

Now, in a right angled triangle using trigonometry, we can determine a side of the triangle is one of the sides and one of the angles is known

Here, if we use cos x = $\frac{Base}{Hypotenuse}$ we can determine the distance between the shooting star and the sun. This can be done because we know that the base is 'y', the angle is x° and the hypotenuse represents the distance between the sun and the shooting star

Note: cos values for each x are definite.