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Find the area of a triangle when A=78°, = 14 and c = 12.

User Asur
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Basically let's use the Law of Sines to solve the given triangle. The Law of Sines is a formula used to find the missing side or angle of a triangle when given the other two sides and one angle. Let us represent the unknown angle B by x.We can use the formula as follows: `a/sin A = b/sin B = c/sin C`We know that: `A = 78°`, `a = 14`, and `c = 12`.So, `a/sin A = c/sin C`=> `14/sin 78° = 12/sin x`=> `sin x = 12(sin 78°)/14`=> `sin x = 0.948`We can find the value of angle B using sine inverse.=> `B = sin^-1(0.948)`=> `B = 72.42°`We can find the value of angle C by using the sum of angles of a triangle.=> `C = 180° - A - B`=> `C = 180° - 78° - 72.42°`=> `C = 29.58°`Now, we can use the formula to find the area of the triangle.Area of the triangle = `1/2 * b * h`Where b = 12 (the base of the triangle) and h = 14 sin 72.42° (the height of the triangle).=> Area of the triangle = `1/2 * 12 * 14 sin 72.42°`=> Area of the triangle = `85.53`Therefore, the area of the triangle is `85.53 square units`.

I know it's kinda confusing, but hope it helped you...

User Bvr
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