A triangle has sides A, B, and C. Sides A and B have lengths of 7 and 8, respectively. The angle between A and C is $\frac{11 π}{24}$ $(11pi)/24$ and the angle between B and C is $\frac{7 π}{24}$ $(7pi)/24$ . What is the area of the triangle?

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Answer 1 · 2016-03-28T05:41:14

Area of triangle is $19.799$ $19.799$

As angle between A and C is $11 \frac{π}{24}$ $11pi/24$ and the angle between B and C is $7 \frac{π}{24}$ $7pi/24$ , angle between A and B is

$π - \frac{11 π}{24} - \frac{7 π}{24} = \frac{6 π}{24} = \frac{π}{4}$ $pi-(11pi)/24-(7pi)/24=(6pi)/24=pi/4$

Area of triangle is given by $\frac{1}{2} a b sin C$ $1/2ab sinC$ and hence it is

$\frac{1}{2} \times 7 \times 8 \times sin (\frac{π}{4}) = \frac{28}{\sqrt{2}} = 19.799$ $1/2xx7xx8xxsin(pi/4)=28/sqrt2=19.799$

A triangle has sides A, B, and C. Sides A and B have lengths of 7 and 8, respectively. The angle between A and C is 11π24(11pi)/24 and the angle between B and C is 7π24 (7pi)/24. What is the area of the triangle?