CPM Homework Help : PC Problem 1-50

To solve a triangle, you need to find all of the missing sides and angles.
Solve $ΔABC$ at right.
(Find $∠A$ , side $b$ , and side $c$ .)

Right triangle, A B C, labeled as follows: Leg, B C 15 cm, Leg, A C, b, hypotenuse, A B, c, angle, B, 38 degrees.

Step 1:

Label all of the sides and angles on the triangle. Always label the sides with the lower case letter of the angle opposite it.

Step 2:

To make this easier, first make a table of sides and angles and fill in the information given.

Step 3:

You have two given angles. How do you get the third angle?

Step 4:

Now that you have all three angles and a side, would you use the Law of Sines or the Law of Cosines to solve for the other two sides?

Answer 1:

Side Angle

$a = 15 A =$
$b = B = 38°$
$c = C = 90°$

Answer 2:

Law of Sines

$\frac{a}{\text{sin}(A)} = \frac{b}{\text{sin}(B)} = \frac{c}{\text{sin}(C)}$

Show all work and solve for the other sides.