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 Earth and the moon. Please explain clearly how the scientist can use only these two measurements to calculate the distance between the Earth and the sun.

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 Earth and the moon. Please explain clearly how the scientist can use only these two measurements to calculate the distance between the Earth and the sun.

anonymous · Answer

here

dumbcow · Answer

you have to use a trig ratio: sin, cos, tan
which one will use y and distance to sun but not the hypotenuse ?

dumbcow · Answer

sin = opp/hyp
cos = adj/hyp
tan = opp/adj

-- only tan does not use hypotenuse, so to solve for distance (adjacent side) we need to use tangent

--> tan(x) = y/d
solve for d
--> d = y/tan(x)

anonymous · Answer

@dumbcow a little bit clearer please

dumbcow · Answer

not sure how to be any clearer...im assuming you've learned trig ratios ?

anonymous · Answer

I'm super confused! I'm doing a practice sheet for my semester exam... I went over them but they didn't stick... :(

dumbcow · Answer

|dw:1337022770878:dw|
an Acronym to use is
SOH CAH TOA

SOH- sin = opp/hyp
CAH - cos = adj/hyp
TOA - tan= opp/adj