CPM Homework Help : PC3 Problem 6-128

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

Hint:

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

Step 1:

Let the missing side be $x$ .

$9^2=23^2+x^2-23x\cos(20^◦)$

Step 2:

$0=x^2-23x\cos(20^◦)+(23^2-9^2)$

Step 3:

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