Question

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


A scientist measures the angle x and the distance y between the Sun and the moon. Using complete sentences, explain how the scientist can use only these two measurements to calculate the distance between the Earth and the moon.

Answer 1

@waterineyes

Answer 2

For angle x,

Distance between Moon and the Earth is : Perpendicular
Distance between Sun and the Moon is : Hypotenuse.

Here, with perpendicular and hypotenuse, you can use, Sine relation..
As :

\[\sin(x) = \frac{Perpendicular}{Hypotenuse} \implies \sin(x) = \frac{Distance \; btwn \; Moon \; and \; Earth}{y}\]

Answer 3

Here, let the distance between earth and moon be : d (it is difficult to write the entire)

So:

\[\sin(x) = \frac{d}{y} \implies \color{green}{d = y \sin(x^\circ)}\]

Answer 4

If you know the measure of angle x and the hypoteneuse, this allows you to solve for the sine of x and figure out the distance between the earth and moon. You'll first get the equation for the sine of x in the following manner: sin(x)=d/y (d = distance). You can then isolate the variable by moving the y over and solve to get the missing side. @waterineyes

Answer 5

is that ok?

Answer 6

It looks fine to me.. :)