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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