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

- The scientist can substitute these measurements into $cos\alpha=\frac{adjacent}{hypotenuse}$ and solve for the distance between the Sun and the shooting star (which would be the hypotenuse of the righ triangle).

Step-by-step explanation:

You can observe in the figure attached that "AC" is the distance between the Sun and the shooting star.

Knowing the distance between the Earth and the Sun "y" and the angle x°, the scientist can use only these two measurements to calculate the distance between the Sun and the shooting star by applying one of the trigonometric functions: Cosine of an angle.

This is:

$cos\alpha=\frac{adjacent}{hypotenuse}$

In this case:

$\alpha=x\°\\\\adjacent=BC=y\\\\hypotenuse=AC$

Therefore, the scientist can substitute these measurements into $cos\alpha=\frac{adjacent}{hypotenuse}$ , and solve for the distance between the Sun and the shooting star "AC":

$cos(x\°)=\frac{y}{AC}$

$AC=\frac{y}{cos(x\°)}$

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