Please help!!!

A shooting star forms a right triangle with the Earth and the Sun, as shown below: A right triangle is shown with the vertices labeled Earth, Sun, and Shooting Star. The angle formed by the Sun is labeled x deg 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. (10 points)

- 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 [tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex] 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:

[tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex]

In this case:

[tex]\alpha=x\°\\\\adjacent=BC=y\\\\hypotenuse=AC[/tex]

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

[tex]cos(x\°)=\frac{y}{AC}[/tex]

[tex]AC=\frac{y}{cos(x\°)}[/tex]

ogorwyne ogorwyne · Answer 2 · 2022-03-28T11:58:28+02:00

The scientist can use the two measurements by applying the knowledge of trigonometry, particularly Cosine (cos).

[tex]cos x = \frac{adjacent (y)}{hypotenuse (AC)}[/tex]

AC = [tex]\frac{y}{cos x}[/tex]

where the distance between the shooting star and the sun is AC

and the distance between Earth and Sun is BC = y

the right angled triangle has three sides

Hypotenuse (hyp): longest side
Opposite (opp): the side facing the angle of interest
Adjacent (adj): the remaining side

cosine (θ) = [tex]\frac{adj}{hyp}[/tex]

sine (θ) = [tex]\frac{opp}{hyp}[/tex]

tan (θ) = [tex]\frac{opp}{adj}[/tex]

where (θ) = angle of interest

What is trigonometry?

This is the branch of mathematics that is concerned with angles of triangles as well as the length of it's sides.

Read more on trigonometry: https://brainly.com/question/24349828