Law of Sines and Cosines Word Problems

Amanda and Jamie are standing 25 feet apart and spot a bird in the sky between them.  The angle of elevation 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. 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

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

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

The dimensions of a triangular lot are 100 feet by 50 feet by 75 feet. If the price of such land is $1 per square foot, how much does the lot cost?

• $1815.461

• $171.163

• It's free!

• $5446.38

What is the area of a triangle with two sides that measure 6 m and 8 m with an included angle of 137°?

• 17.8m²

• 14.6m²

• 16.4m²

• 12.9m²