Law of Sine and Cosine Word Problems

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

A triangular parcel of land with vertices at R, S, and T was to be enclosed by a fence, but it was discovered that the surveyor’s mark S was missing. From a deed to a property, it was learned that the distance from T to R is 324 meters, the distance from T to S is 506 meters, and the angle at R in the triangle is 125.4 degrees. Determine the location of S by finding the distance from R to S.

• 205 meters

• 211 meters

• 222 meters

• 244 meters

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

• 152.7 feet

• 166.3 feet

• 157.3 feet

• 131.7 feet

Round your answer to the nearest tenth.

• 1747.5 ft.

• 1319.3 ft.

• 1428.2 ft.

• 2747.5 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

Use law of Sines to find side c.

Round your answer to the nearest hundredth

Mathematical Equivalence

OFF

Round your answer to the nearest tenth.

• 36.9^°

• 31.0^°

• 59.0^°

• 53.1^°