Question

The moon forms a right triangle with the Earth and the Sun during one of its phases, as shown below:

Answer 1

Answer:

The scientist can calculate the distance between the moon and the sun using trigonometric ratio of Cosine.

Step-by-step explanation:

We have been given that the moon forms a right triangle with the Earth and the Sun during one of its phases.

We can see from our graph that the distance between Sun and Moon is the hypotenuse of the right triangle as it is the opposite side of right angle formed with the Earth.

The distance between Earth and Sun (y) is the adjacent side for our angle x degrees.

Since we know that the cosine of an angle is the trigonometric ratio of the adjacent side to the hypotenuse of a right triangle containing that angle.

$\text{Cos}=\frac{\text{Opposite}}{\text{Hypotenuse}}$

$\text{Cos}(x^o)=\frac{y}{\text{The distance between Sun and Moon}}$

$\text{The distance between Sun and Moon}=\frac{y}{\text{Cos}(x^o)}$

Therefore, using trigonometric ratio Cosine, the scientist can calculate the distance between the Moon and the Sun.