SOLUTION: The area of a triangle is equal to 49 sq cm and two of its sides measure 17 cm and 16 cm. Find the possible measure of the included angle in degrees of the given sides.

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Question 1150872: The area of a triangle is equal to 49 sq cm and two of its sides measure 17 cm and 16 cm. Find the possible measure of the included angle in degrees of the given sides.
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
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Use the formula for the area of a triangle 


    S = %281%2F2%29%2Aa%2Ab%2Asin%28gamma%29


where "a" and "b" are two any side lengths of the triangle and  gamma  is the concluded angle between them.


From the formula,  sin%28gamma%29 = %282%2AS%29%2F%28a%2Ab%29 = %282%2A49%29%2F%2817%2A16%29 =  0.360.


Hence,  gamma = arcsin%280.360%29 = 0.368583 radians = 21.118 degrees.


The other possible value for the angle  gamma  is 180 degrees MINUS  21.118 degrees = 158.882 degrees.


ANSWER.  At given conditions, there are two possible values for the angle between the sides  

         21.118 degrees  OR  158.882 degrees (approximately).

Solved.

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It is just SECOND TWIN problem posted and solved today.

Please do not post twin problems.


Thank you very much.