CPM Homework Help : CCG Problem 5-126

A triangle with side lengths 17 and 10. A 45 degrees angle is between the two sides. Solve for the missing side lengths and angles in the triangle at right.

Hint:

This triangle has known values for $\text{SAS}$ (side-angle-side) so will need to be solved using the Law of Cosines.
Refer to the Math Notes box in Lesson 5.3.3 if you need help remembering the Law of Cosines.

Triangle, A B C, labeled as follows: side, A B, small letter c, side, B C, 10, side, A C, 17.

Step 1:

Solve for $c$ .

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

Step 2:

After finding the length of $c$ , the Law of Sines can be used to to find the measure of $∠A$ .
Refer to the Math Notes box in Lesson 5.3.2 for the Law of Sines.

$\frac{\text{sin }A}{10}=\frac{\text{sin }45}{c}$

Step 3:

Use the Triangle Angle Sum Theorem to find the measure of $∠B$ .