# A triangle has sides A, B, and C. Sides A and B have lengths of 7 and 9, respectively. The angle between A and C is (pi)/8 and the angle between B and C is  (pi)/24. What is the area of the triangle?

Apr 7, 2018

$\text{Since " color(brown)(a / sin A != b / sin B), color(crimson)(" we can not form a triangle with the given measurements.}$

#### Explanation:

As per the Law of Sines, $\frac{a}{\sin} A = \frac{b}{\sin} B$

$\frac{a}{\sin} A = \frac{7}{\sin} \left(\frac{\pi}{24}\right) = 53.63$

$\frac{b}{\sin} B = \frac{9}{\sin} \left(\frac{\pi}{8}\right) = 23.52$

$\text{Since " color(brown)(a / sin A != b / sin B), color(crimson)(" we can not form a triangle with the given measurements.}$

Apr 7, 2018

color(purple)("Inconsistency in the given measurements according to the Greater Angle and Greater Side Theorem"

#### Explanation:

$\text{As per the Greater Angle and Greater Side Theorem'}$

$b > a , \text{if and only if } \hat{B} > \hat{A}$

$\text{Since " hat B < hat A, " though " b > a, " we cannot form a triangle with the given measures.}$