Word Problem Exercises: Law of Sines

A flagpole is situated on a hill that makes an angle of 18° with the horizontal. How tall is the flagpole if its shadow is 14 meters when the angle of elevation of the sun is 31°?

The course for a bike race follows a triangular shaped trail. The first leg is a straight 6 kilometer ride. After that, the biker must turn 283° to the left and follow the trail to the next turn. Turning 269° again to the left will take the biker to the finish line, which is exactly where he started. How long is the entire race?

The angle of elevation to the top of a building is 21°. At a point 80 feet closer, the angle of elevation to the top of the same building is 33°. Approximate the height of the building.

You are taking a flight from Daytona Beach to St. Louis. There is a stopover in Atlanta. The bearing from Daytona Beach to Atlanta is N 38.3° W. The bearing from Daytona straight to St. Louis is N 43.4° W . The distance of the first leg of the trip from Daytona to Atlanta is approximately 599.8 kilometers. From Atlanta to St. Louis is another 748.4 kilometers.

What is the total length of the trip with the stopover?
How much shorter would it be to fly straight to St. Louis from Daytona Beach without a stopover?

Two people are walking toward each other on a path through the park. The path runs east and west. A hot air balloon is directly above the path between them. One of the walkers, a female, sees the balloon when looking east at an angle of elevation of 46°. The other walker, a male, sees the balloon looking west at an angle of elevation of 72°. If the walkers are 55 yards apart, how far is the balloon from the male observer?