# A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 5, respectively. The angle between A and C is (5pi)/24 and the angle between B and C is  (pi)/24. What is the area of the triangle?

Aug 12, 2017

No such triangle exists. Please see the explanation.

#### Explanation:

I shall use the notation where the lengths of the sides are in lower case letters and the angles opposite the sides are in the corresponding upper case letter.

The phrase "Sides A and B have lengths of 5 and 5" gives us this information:

$a = b = 5$

The phrase "The angle between A and C is $\frac{5 \pi}{24}$" gives us this information:

$B = \frac{5 \pi}{24}$

The phrase "the angle between B and C is $\frac{\pi}{24}$" gives us this information:

$A = \frac{\pi}{24}$

This cannot be! Because $a = b$, $A$ must equal $B$ but we are told that this is not true, therefore, no such triangle exists.