A triangle has a 56-degree angle, formed by a 10-inch side and an x-inch side. Given that the area of the triangle is 18 square inches, find x.
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One of the formulas for the area of a triangle is given by:
Where C is an angle and a and b are the sides of the angle.
Use the law of cosines to find the length of the third side in terms of x. Then apply Heron's Formula:
where A is the area, s is half of the perimeter, and a, b, and c are the sides. Edit: Chop Suey's method is much easier.
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