Law of Cosines Word Problems

Lucas 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 boards joined at the top at a 45^o angle. To prevent the swing set from tipping over, Lucas wants to secure the base of each A-frame to concrete footings in the ground. How far apart should the footings for each A-frame be?

• 7.21 ft

• 7.65 ft

• 8.11 ft

• 6.91 ft

Emma and Alyssa are 20 miles apart and spot a UFO in the sky between them. The angle of elevation 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