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Use Law Of Cosines To Solve Real Life Problems

 A plane flying directly above a post 6000m away from an anti-aircraft gun observes the gun at an angle of depression of 27̊. Find the height of the plane.

Randy is training for a marathon. He starts his journey by running 9 miles in one direction. Then, he turns and runs another 11 miles. The two legs of his run form an angle of 79o. How far is Randy from his starting point at the end of the 11-mile leg of his run?

  A plane travels 800 meters along the runway before taking off at an angle of 10 degrees. It travels a further 1,000 meters at this angle as seen in the figure. Work out the distance of the plane from its starting point.

 Find the step angle X made by the hindfoot of a person whose pace averages 30 inches and stride averages 35 inches.

 A ladder leaning against a vertical wall makes an angle of 24̊ with the wall. Its foot is 5m from the wall. Find its length?

 Two cars leave a city at the same time and travel along straight highways that differing direction by 80. One car averages 60 miles per hour and the other averages 50miles per hour. How far apart will the cars be after 90 minutes?

  A vertical pole is 8m high and the length of its shadow is 6m. what is the angle of elevation of the sun at the moment?

At the top of a cliff 80m high, the angle of depression of boat is 12̊.How far is the boat from the cliff?

 Find the step angle X made by the hindfoot of a person whose pace averages 27 inches and stride averages 32 inches.

 When the angle between the ground and the sun is 30̊, flag pole casts a shadow of 40m long. Find the height of the top of the flag?