### Home > PC3 > Chapter 6 > Lesson 6.2.4 > Problem6-128

6-128.

In a triangle, $A=20°$, $a=9$, and $b=23$. Solve the triangle.

The given information is SSA, so use the Law of Cosines to determine the possible number of triangles.

Let the missing side be $x$.

$9^2=23^2+x^2-23x\cos(20^◦)$

$0=x^2-23x\cos(20^◦)+(23^2-9^2)$

Use the Quadratic Formula to solve for the possible lengths of the missing side.
$a = 1$
$b=−23\cos\left(20^{\circ}\right)$
$c = 23^{2} − 9^{2}$