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The tower you were supposed to fix has lost all of its screws! i thought i told you to fix it!
I thought i did, sorry boss i will get back to work immediately.
Later Fred is out on the town when he runs into his boss!
His boss is not happy...
Fred sets off to get to work once again.
When Fred gets to the tower he notices that the screws are forming a triangle. Fred decides to use his knowledge of the law of sine to figure out one of the unknown side lengths of the triangle. Fred knows that the left most side of the triangle is 12 feet long. He also knows that the bottom angle is 71 degrees, and the right most angle is 35 degrees. Fred sets up the equation sin35/12=sin71/x, and concludes that x=19.8.
As Fred picks up the screws to put them back in the tower, he drops all of them again, creating anew triangle. Fred once again has a burning desire to use his trigonometry skills to find the unknown side length. This time however Fred decides to use the law of cosine. Fred now knows that the left most side is 7 feet long, and the right most side is 12 feet long. he also knows that the top most angle is 65 degrees. Fred creates this expression to demonstrate. x(x)=7(7)+12(12)-2(7)(12)cos65. Fred can then find out that x=11.04.
Fred feels very accomplished, and smarter after solving those two thought provoking problems. Now Fred must put the screws back. In order for Fred to get to the correct spot on the tower he must find out the angle to the spot he is trying to go to. Fred knows that the height from the base of the tower to the spot he must go to is 15 feet, and from the spot to his feet is 20 feet. he wants to know the angle that is being formed by the ground, and the height between the spot and the ground. he creates (cosx=15/20)cos-1, and concludes that x=41.4 degrees
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