Law of Cosines and Law of Sines Sides

Set up the law of cosines to find side XZ.

Find side QR.

• 34.7 km

• 2.2 km

• 13.74 km

• 31.1 km

Set up the law of sines to find side AB.

Find the angle at B.

• 35

• 209

• 87

• 29

Solve the law of sines to find the length of side BC. \frac{\sin\left(93\right)}{BC}=\frac{\sin\left(29\right)}{16}

Which equation could NOT be used to find x?

(Choose the equation that is set up incorrectly.)

If a triangle has 1 angle and 2 sides, there are often two possible triangles. You solve law of sines to find the first possible angle for the triangle. How do you find the second possible angle?

• Subtract your first answer from 180^o

• Subtract your first answer from 360^o

• Add your first answer to 180^o

• Subtract the angle on the triangle from your first answer

A triangle has side lengths 46 and 31. The angle opposite the side with length 46 measures 53 degrees.

Which equation can be used to find the angle opposite the side with length 31?

A triangle has side lengths 46 and 31. The angle opposite the side with length 46 measures 53 degrees. Solve for x to find a possible measure of the angle opposite the side with length 31. (Round to the nearest degree.) \frac{46}{\sin\left(53\degree\right)}=\frac{31}{\sin\left(x\right)}

A triangle has side lengths 46 and 31. The angle opposite the side with length 46 measures 53 degrees. Find the possible measure(s) of the angle opposite the side with length 31. (Round to the nearest degree.)