Law of Cosines Word Problems

Amanda and Jamie are standing 25 feet apart and spot a bird in the sky between them. The angle from Amanda to the bird is 55, and from Jamie to the bird is 63. How far away is the bird from Amanda?

• 25.23

• 23.19

• 22.15

• 20.85

Two stakes are holding a small blimp in place in the air. Stake A to the rope is an angle of 49^o and Stake B to the rope is an angle of 58^o. If the rope attached to Stake A has a length of 148 feet, what is the length of the rope attached to Stake B?

• 152.7 feet

• 166.3 feet

• 157.3 feet

• 131.7 feet

Emma and Alyssa are 20 miles apart and spot a UFO in the sky between them. The angle from Emma to the UFO is 15^o, and from Alyssa to the UFO is 35^o (see diagram). How far away is the UFO from Emma?

• 6.76 mi

• 12.36 mi

• 14.98 mi

• 17.59 mi

Mr. Creole must find the distance from Point A to Point B on opposite sides of a lake. He locates Point C that is 4.15 miles from point A and 5.33 miles from Point B. He measures the angle ACB to be 37^o. Find the distance from point A to point B.

• 3.72 miles

• 6.18 miles

• 10.30 miles

• 3.21 miles

A GPS satellite measures the distances to two buildings to be 370 km and 350 km, and the angle between them to be 2.1^o (see diagram). How far apart are the two buildings?

• 17.90 km

• 30.32 km

• 15.61 km

• 23.96 km

Two cruise ships leave the same port with a 35° angle between their path. Cruise A is traveling

at 18 miles per hour and Cruise B is traveling at 15 miles per hour. If they travel in a straightpath, find the distance between the cruise ships after 2 hours. Round to the nearest tenth of a mile.

A pole is supported by two wires, one on each side, going in opposite directions. The wires are 14 feet and 17 feet long. If the wires are to be secured to the ground 22 feet from each other, what angle must the 14-foot long wire make with the ground? Round to the nearest degree.