Law of Sines and Cosines

What is the length of side x?

• 130 cm
• 112 cm
• 150 cm
• 105 cm

What is the measure of angle A?

• 50 degrees
• 60 degrees
• 78 degrees
• 74 degrees

Use the Law of Sines to solve for BC

• 33
• 24
• 12
• 29

Find angle A

• 53.6
• 13.3
• 113.1

Use the Law of Cosines to find the value of x. 

• 41.7
• 51.7
• 61.7
• 71.7

Clint is building a wooden swing set for his children.  Each supporting end of the swing set is to be an A-frame constructed with two 10 foot long 4-by-4s joined at a 45 degree angle.  To prevent the swing set form tipping over, Clint wants to secure the base of each A-frame to concrete footings.  How far apart should the footings for each A-frame be?

• 5.461 feet
• 9.743 feet
• 6 feet
• 7.65 feet

Jack is flying his kite.  He runs 100 feet away from his house and lets out 75 feet of string.  The angle of elevation from the ground to the kite is 65 degrees.  How far away is the kite from the house?

• 9285.73 ft
• 96.36 ft
• 24061.81 ft
• 155.12 ft

Find the area

• 26.5 in²

• 28.8 in²

• 12.5 in²

• 25.1 in²

Two radar stations 2.5 miles apart are tracking an airplane. the straight-line distance between Station A and the plane is 7 miles. the straight-line distance between station B and the plan is 9 miles. What is the angle of elevation from Station B to the plane?

• 28 degrees

• 32 degrees

• 36 degrees

• 40 degrees

Three boats are out at sea: Boat A, Boat B, and Boat C. The crew of Boat A can see both Boat B and Boat C. The angle between the line of sight to Boat B and the line of sight to Boat C is 49°. If the distance between Boat A and Boat B is 1.8 miles and the distance between boat A and Boat C is 3.2 miles, what is the distance between Boat B and Boat C?

• 2.4 miles

• 5.3 miles

• 1.3 miles

• 3.7 miles