A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 2, respectively. The angle between A and C is (5pi)/24 and the angle between B and C is (pi)/24. What is the area of the triangle?

1 Answer
Shwetank Mauria
Mar 14, 2016

3.5355

Explanation:

The angle between A and C is (5pi)/24 and the angle between B and C is pi/24, Hence, angle between A and B is pi-(5pi)/24-pi/24=(24-5-1)pi/24=(18pi)/24=(3pi)/4

As sides A and B have lengths of 5 and 2 angle between them is (3pi)/4,

Area of the triangle is given by the formula 1/2bcsinA

and hence it is 1/2xx5xx2xxsin(3pi)/4

= 1/cancel(2)xx5xxcancel(2)xxsqrt2/2

= 5xx1.4142/2=5xx0.7071=3.5355

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