1. Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. (If an answer does not exist, enter DNE. Round your answers to one decimal place. Below, enter your answers so thatA₁is smaller thanA₂.)

b=24, c=31, B=27

a1=

a2=

2. Use the Law of Cosines to determine the indicated angle . (Assume a = 61.01, b = 39.86, and c = 42.05. Round your answer to two decimal places.) =

3. Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place.)

b = 65, c = 39, A = 74

a=

4. Find the indicated side x. (Use either the Law of Sines or the Law of Cosines, as appropriate. Assume A = 32 and C = 88. Round your answer to two decimal places.) x =

5. Find the indicated angle . (Use either the Law of Sines or the Law of Cosines, as appropriate. Assume

a = 12,

c = 11,

and

C = 50.

Round your answer to one decimal place. Assume that is greater than 90.) =

6. Find the area A of the triangle whose sides have the given lengths.

a = 20, b = 15, c = 25

A =

7. Find the area of the triangle whose sides have the given lengths. (Round your answer to one decimal place.)

a = 8, b = 11, c = 14

A =

8. To find the distance across a small lake, a surveyor has taken the measurements shown. Find the distance across the lake using this information. (Assume points A and B are exactly along the shoreline, and that a = 2.62 miles and b = 3.11 miles. Round your answer to two decimal places.)

9. A car travels along a straight road, heading east for 1 h, then traveling for 30 min on another road that leads northeast. If the car has maintained a constant speed of 32 mi/h, how far is it from its starting position? (Round your answer to one decimal place.)