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Chapter 8: Q. 15 (page 535)
Solve the triangle
The solution is
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Finding the Length of a Ski Lift Consult the figure. To find the length of the span of a proposed ski lift from P to Q, a surveyor measures DPQ to be 25掳 and then walks off a
distance of 1000 feet to R and measures PRQ to be 15掳. What is the distance from P to Q?
Mollweide鈥檚 Formula For any triangle, Mollweide鈥檚 Formula (named after Karl Mollweide, 1774鈥�1825) states that
Derive it.
[Hint: Use the Law of Sines and then a Sum-to-Product Formula. Notice that this formula involves all six parts of a triangle. As a result, it is sometimes used to check the solution of a triangle.]
A person in a small boat, offshore from a vertical cliff known to be feet in height, takes a sighting of the top of the cliff. If the angle of elevation is found to be, how far offshore is the boat?
Designing an Awning An awning that covers a sliding glass door that is 88 inches tall forms an angle of 50掳 with the wall. The purpose of the awning is to prevent sunlight from entering the house when the angle of elevation of the Sun is more than 65掳. See the figure. Find the length L of the awning.
A security camera in a neighborhood bank is mounted on a wall 9 feet above the floor. What angle of depression should be used if the camera is to be directed to a spot 6 feet above the floor and 12 feet from the wall?
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