SOLUTION: If there is a right triangle ABC and AB is 6 cm, angle A is 15 degrees, angle B is 90 degrees, and angle is 75 degrees? What is the area in simplest radical form?

Question 145854: If there is a right triangle ABC and AB is 6 cm, angle A is 15 degrees, angle B is 90 degrees, and angle is 75 degrees? What is the area in simplest radical form?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
If there is a right triangle ABC and AB is 6 cm, angle A is 15 degrees, angle B is 90 degrees, and angle is 75 degrees? What is the area in simplest radical form?
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Draw a diagram of the triangle and label the sides and angles.
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Applying trig, you would use:
tan = opposite/adjacent
tan(15) = height/6
height = 6tan(15)
height = 6(2-sqrt(3))
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area of a triangle = 1/2 * height * base
area of a triangle = 1/2 * 6(2-sqrt(3)) * 6
area of a triangle = 3(2-sqrt(3)) * 6
area of a triangle = 18(2-sqrt(3))

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