# A triangle has sides A, B, and C. Sides A and B have lengths of 6 and 1, respectively. The angle between A and C is (13pi)/24 and the angle between B and C is  (3pi)/8. What is the area of the triangle?

Feb 6, 2016

$= 2.97 {\text{ units}}^{2}$ to 2 decimal places

$\textcolor{red}{\text{ The question has an error! }}$Producing the diagram to scale using just the angles shows that it is C that is 1. NOT B.

#### Explanation:

$\textcolor{p u r p \le}{\text{This gave me a lot of trouble until I drew the diagram near enough to scale!}}$

$\textcolor{b l u e}{\text{Assumption: The angles given in relation to the sides is correct.}}$

$\textcolor{red}{\text{Consequently the length of B is not 1}}$

$\textcolor{red}{\text{It is the length of C that is 1}}$
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$\text{Area } = \frac{C}{2} A \sin \left(\frac{13 \pi}{24}\right)$

$= \frac{1}{2} \times 6 \times \sin \left(\frac{13 \pi}{24}\right)$

$= 2.97 {\text{ units}}^{2}$ to 2 decimal places