A triangle has sides A, B, and C. Sides A and B have lengths of 1 and 3, respectively. The angle between A and C is $(13pi)/24$ and the angle between B and C is $(pi)/24$ . What is the area of the triangle?

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Answer 1 · 2016-04-15T07:37:06

Area of triangle is $1.449$ units.

The formula for area of a triangle given two sides $a$ and $b$ and included angle $theta$ is $1/2xxabxxsintheta$ .

Here, though we have been given two sides as $1$ and $3$ , included angle has not been given.

But as other two angles are $(13pi)/24$ and $pi/24$ , third angle will be given by

$pi-(13pi)/24-pi/24=(24pi-13pi-pi)/24=(10pi)/24$

Hence area of triangle is $1/2xx1xx3xxsin((10pi)/24)$

= $3/2xx0.9659=1.449$ units.

A triangle has sides A, B, and C. Sides A and B have lengths of 1 and 3, respectively. The angle between A and C is (13pi)/24(13pi)/24 and the angle between B and C is (pi)/24 (pi)/24. What is the area of the triangle?