SOLUTION: 10. Given:  triangle  ABC below.  AB = 5 AC = 8 BC = 6 A. Find m∠A in the triangle. B. Find the area of the triangle.

Algebra ->  Trigonometry-basics -> SOLUTION: 10. Given:  triangle  ABC below.  AB = 5 AC = 8 BC = 6 A. Find m∠A in the triangle. B. Find the area of the triangle.       Log On


   

Question 1206021: 10. Given:  triangle  ABC below. 
AB = 5
AC = 8
BC = 6
A. Find m∠A in the triangle.

B. Find the area of the triangle.

Answer by ikleyn(52919) About Me  (Show Source):
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10. Given:  triangle  ABC below. 
AB = 5
AC = 8
BC = 6
A. Find m∠A in the triangle.
B. Find the area of the triangle.
~~~~~~~~~~~~~~~~~~~~ 

(A)  Use the cosine law for the side "a" opposite to angle A

         a%5E2 = b%5E2+%2B+c%5E2+-+2bc%2Acos%28A%29,  a = BC = 6;  b = AC = 8;  c = AB = 5:

         6%5E2 = 8%5E2+%2B+5%5E2+-+2%2A8%2A5%2Acos%28A%29.


     It gives  cos(A) = %288%5E2+%2B+5%5E2+-+6%5E2%29%2F%282%2A8%2A5%29 = 53%2F80 = 0.6625;
           
                   A = arccos(0.6625) = 48.51 degrees = 48 degrees and 31 minutes  (rounded).    ANSWER



(B)  Use the Heron's formula

         area of a triangle = sqrt%28s%2A%28s-a%29%2A%28s-b%29%2A%28s-c%29%29,

                               where "s" is semi-perimeter = %285%2B8%2B6%29%2F2 = 9.5 units.

         area of the triangle = sqrt%289.5%2A%289.5-5%29%2A%289.5-6%29%2A%289.5-8%29%29 = 14.98 square units  (rounded).    ANSWER

Solved.