SOLUTION: The lengths of segments PQ and PR are 8 inches and 5 inches, respectively, and they make a 60-degree angle at P. Find the third side of another triangle that has a 5-inch side, an

Algebra ->  Triangles -> SOLUTION: The lengths of segments PQ and PR are 8 inches and 5 inches, respectively, and they make a 60-degree angle at P. Find the third side of another triangle that has a 5-inch side, an       Log On


   

Question 1163756: The lengths of segments PQ and PR are 8 inches and 5 inches, respectively, and they make a 60-degree angle at P. Find the third side of another triangle that has a 5-inch side, an 8-inch side, and the same area as triangle PQR.
Answer by ikleyn(52914) About Me  (Show Source):
You can put this solution on YOUR website!
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Use the formula for the area of the triangle via the lengths of its any two side lengths and the angle between them


    Area = %281%2F2%29%2Aa%2Ab%2Asin%28alpha%29.


From this formula, conclude that the other triangle, having the same area as the given triangle, has the angle of 120 degrees
between two sides of the length 8 inches and 5 inches.


Then apply the cosine law to calculate the length of the third side


    sqrt%285%5E2+%2B+8%5E2+-+2%2Acos%28120%5Eo%29%29 = sqrt%285%5E2+%2B+8%5E2+-+2%2A%28-1%2F2%29%29 = sqrt%2825+%2B+64+%2B+1%29 = sqrt%2890%29 = 3%2Asqrt%2810%29 = 9.487 inches (approximately).    ANSWER

Solved.