SOLUTION: How do you find the area of a 30,60,90 triangle with a height of 4 inches and an unknown base? P.S. the answer must be a radical number

Question 541207: How do you find the area of a 30,60,90 triangle with a height of 4 inches and an unknown base?
P.S. the answer must be a radical number

Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
Area = 1/2 * Base * Height
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Height = 4 (given)
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The triangle is a 30-60-90. (given)
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The 30-60-90 triangle is a special triangle that most students have to learn to manipulate.
The sides of the triangle have a well-known relationship.
The side opposite the 30 degree angle is the short side.
The side opposite the 90 degree angle is the hypotenuse. It is twice the length of the short side.
Applying the Pythagorean Theorem, we can calculate the third side. It will have a sqrt(3) component.
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The relationships can be used to define the lengths of the sides.
Let's call the short side S for "short".
Call the hypotenuse H.
Call the third side L for "long" because it is longer than S. Of course, it is shorter than H.
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Therefore, we can determine:
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In what may be a typical layout, the L side is shown vertically, which makes it the height.
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From the last equation (above), we can deduce that:
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That means:
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Done.
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