Question

The moon forms a right triangle with the Earth and the Sun during one of its phases, as shown below: A right angle triangle is shown with the Earth at the right angle. The acute angle between the line joining the Earth and the Sun and the Sun and the moon is x degrees. The distance between the Earth and the moon is y. A scientist measures the angle x and the distance y between the Earth 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 Sun.

Answer 1

Answer:

Distance Between Earth & Sun = yCotx°

Step-by-step explanation:

The moon forms a right triangle with the Earth and the Sun during one of its phases, as shown below: A right angle triangle is shown with the Earth at the right angle. The acute angle between the line joining the Earth and the Sun and the Sun and the moon is x degrees. The distance between the Earth and the moon is y. A scientist measures the angle x and the distance y between the Earth 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 Sun.

Tan θ = Perpendicular / Base

Here Tan x° =  Distance Between Moon & Earth / Distance Between Earth & Sun

=> Tan x° = y/Distance Between Earth & Sun

=> Distance Between Earth & Sun = y/Tanx°

=> Distance Between Earth & Sun = yCotx°

Answer 2

To find :

The distance between the Earth and the Sun.

Solution :

Let us assume d be the distance between moon and sun.

d is the hypotenuse of a right triangle.

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.

The distance y is the side opposite to angle x in the right triangle.  

By using the definition from trigonometry for sin function,

we get,

sin(x) = y/d ⇒   d = y/sin(x)