Consider the triangle at right.

1. Solve for the missing side lengths and angles in the triangle.

   Hint (a):

   This triangle has known values for SAS (side-angle-side) so will need to be solved using the Law of Cosines.
   Refer to the Math Notes box in Lesson 7.2.3 if you need help remembering the Law of Cosines.

   Step 1 (a):

   Solve for the missing side length.

   $c^{2}=10^{2}+17^{2}-2(10)(17)\text{ cos }45^\circ$

   Step 2 (a):

   After finding the length of $c$, the Law of Sines can be used to to determine the missing angle measures. Refer to the Math Notes box in Lesson 7.2.2 for the Law of Sines.

   $\frac{\sin A}{10}=\frac{\sin 45^\circ}{c}$

2. What is the area of the triangle?

   Hint (b):

   Drawing in the height creates a special right triangle.

   Using the special relationship, determine the height of the triangle.