# Sin 2 θ 2 final exammac1114 page 7 of 8 24 10 pts to

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sin 2 ( θ /2) =

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Final Exam/MAC1114 Page 7 of 8 24. (10 pts.) To measure the height of the top of a distant object , a surveyor takes two sightings of the top of the object 5000 feet apart. The first sighting, which is nearest the object, results in an angle of elevation of 45°. The second sighting, which is most distant from the object, results in an angle of elevation of 30°. If the transit used to make the sightings is 5 feet tall, what is the height of the object. You may assume the object is on a level plane with the base of the transit. 25. (15 pts.) Sketch the given curve in polar coordinates. Do this as follows: (a) Carefully sketch the auxiliary curve, a rectangular graph on the coordinate system provided. (b) Then translate this graph to the polar one. Equation: r = 1 + 2 sin( θ ) (a) r θ (b) y x
Final Exam/MAC1114 Page 8 of 8 26. (10 pts.) Very carefully sketch the graph of the equation (x + 1) 2 = -4(y - 2) below. y x 27. (5 pts.) Use the Law of Sines to solve the triangle with α = 115°, γ = 30°, and c = 3. You may assume that the standard labelling scheme is used. 28. (10 pts.) Very carefully sketch the graph of the equation (y + 1) 2 - (x + 2) 2 = 1 below. y x
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• Spring '08
• Storfer
• Trigonometry, Tan, pts, Final Exam/MAC1114

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