Question

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

Answer 1

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: Cosine of an angle.

- The scientist can substitute these measurements into $cos\alpha=\frac{adjacent}{hypotenuse}$ and solve for the distance between the Earth and the Sun.

Step-by-step 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: Cosine of an angle.

The scientist can substitute these measurements into  $cos\alpha=\frac{adjacent}{hypotenuse}$, and solve for the distance "d".

Knowing that:

$\alpha=x\°\\adjacent=d\\hypotenuse=y$

Then:

$cos(x\°)=\frac{d}{y}$

And solving for "d":

$ycos(x\°)=d$