Applications of Laws of Sines and Cosines

Joey must find the distance from Point A to Point B on opposite sides of a lake. He locates Point C that is 860 feet from point A and 175 feet from Point B. He measures the angle at Point C to be 78 degrees. Find the distance from point A to point B.

• 707643.58

• 841.22

• 877.62

• 845.01

Solve for the missing distance

• 18.9 meters
• 19.5 meters
• 47.2 meters
• 27.5 meters

A yacht is anchored 90 feet offshore from the base of a lighthouse.  The angle of elevation from the boat to the top of the lighthouse is 26 degrees.  The distance between the yacht and the top of the lighthouse is about 100 feet.  Which of these is nearest to the height of the lighthouse? 

• 23 feet
• 43 feet 
• 110 feet 
• 135 feet 

A tourist views a deer from a height of 45 feet.  The horizontal distance between the tourist and the deer is 130 feet.  At what angle (x) should the tourist hold his camera to photograph the deer? Round your answer to the nearest degree.  

• 19 degrees
• 45 degrees
• 71 degrees
• 138 degrees 

What would be used to find the distance (x) across the lake?

• Quadratic Formula
• Law of Cosines
• Law of Sines
• Trigonometric Ratios

What would be used to find the distance from the Ranger's Tower to the fire?

• Quadratic Formula
• Law of Cosines
• Law of Sines
• Trigonometric Ratios

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
• 96.36
• 24061.81
• 155.12

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 degrees, and from Jamie to the bird is 63 degrees.  How far away is the bird from Amanda?

• 25.23
• 23.19
• 22.15
• 20.85

Clint 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 a 45 degree angle.  To prevent the swing set from tipping over, Clint wants to secure the base of each A-frame to concrete footings.  How far apart should the footings for each A-frame be?

• 5.461 feet
• 9.743 feet
• 6 feet
• 7.65 feet