SOLUTION: The diagonal and the longer side of a rectangle make an angle of 30 degree. If the longer side is 10m,find the length of the shorter side.

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Question 968939: The diagonal and the longer side of a rectangle make an angle of 30 degree.
If the longer side is 10m,find the length of the shorter side.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) (Show Source):
You can put this solution on YOUR website!
h, hypotenuse
L, longer side
s, shorter side

but is this necessary?

You have a Special 30-60-90 Right Triangle, so you already can rely on some facts, again which you can find through use of Pythagorean Theorem. Alternatively, the long leg is the height of an equilateral triangle and the hypotenue (or diagonal) is one of the sides of the equilateral triangle. You can therefore form this:

......but again, is this the only necessary way?

WHAT YOU REALLY WANT IS HERE:

You know the sine and the cosine of 30 degrees.

The question is for finding the shorter leg, s.

Use this in the other, the sine equation.....

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You can fill in the values and compute.

Answer by MathTherapy(10552) (Show Source):
You can put this solution on YOUR website!
The diagonal and the longer side of a rectangle make an angle of 30 degree.
If the longer side is 10m,find the length of the shorter side.

This represents a 30-60-90 special triangle with the known side (10 m) being the longer leg, since it's opposite the larger acute angle ().
With longer leg being 10 m, shorter leg = , or m