A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 7, respectively. The angle between A and C is $(pi)/12$ and the angle between B and C is $(2pi)/3$ . What is the area of the triangle?

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Answer 1 · 2016-02-10T16:28:39

Area is $12.3745$ .

Formula for area of a triangle in terms of its two sides is half the product of two sides multiplied by sine of the angle between the two sides.

Here we have sides A and B, but we do not know the angle between them.

Fr this, as sum of internal angles of a triangle is $pi$ and other two angles are $pi/12$ and "2pi/3#,

third angle is $pi - pi/12 - (2pi)/3$ i.e. $(3pi)/12$ or $pi/4$

Hence, as $sin (pi/2)$ is $(1/sqrt2)$

Area of triangle is $(1/2)*5*7*sin (pi/4)$

or $(1/2)*5*7*(1/sqrt2)$ ,

i.e. $12.3745$

A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 7, respectively. The angle between A and C is (pi)/12(pi)/12 and the angle between B and C is (2pi)/3 (2pi)/3. What is the area of the triangle?