Law of Sines and Cosines Applications

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

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

In an effort to recover Abraham's lost cell phone, two cell towers stationed 6000 feet apart detect the signal from the phone. Using strength of signal, the west tower measures the phone to be 5050 feet away and the east tower detects the phone to be 2420 feet away (see diagram). What angle  $\theta$  should Abraham walk from the west tower to get to his phone?

•  $\theta=18.48\degree$  

•  $\theta=23.33\degree$  

•  $\theta=24.17\degree$  

•  $\theta=27.91\degree$  

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.

Which Law would you use?

• Law of Sines
• Law of Cosines
• Law of the Jungle
• Law of Gravity

Which Law would you use?

• Law of Sines
• Law of Cosines
• Law of the Jungle
• Law of Gravity

Which Law would you use?

• Law of Sines
• Law of Cosines
• Law of the Jungle
• Law of Gravity