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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.

A shooting star forms a right triangle with the Earth and the Sun, as shown below-example-1
User Scniro
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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 =
(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.

User Fsperrle
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