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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- Oct 7th 2008, 06:15 PMpyrosilvertriangle trig
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.

- Oct 7th 2008, 06:19 PMChop Suey
One of the formulas for the area of a triangle is given by:

$\displaystyle A = \frac{1}{2}ab\sin{C}$

Where C is an angle and a and b are the sides of the angle. - Oct 7th 2008, 06:20 PMicemanfan
Use the law of cosines to find the length of the third side in terms of x. Then apply Heron's Formula: $\displaystyle A = \sqrt{s(s - a)(s - b)(s - c)}$

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.