An enemy covenant jet fighter just landed on a

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An enemy Covenant jet fighter just landed on a smaller island across the water. Master Chief would like to fire a shell across the water directly at the jet. However, as the Scorpion Tank can only launch a shell a maximum horizontal distance of 3.3 miles, Master Chief might be unable to hit his target. He has decided to calculate the distance to the jet. For his calculation, he measured five distances. Starting at a rock at point R , he drove his tank along a straight path in the direction of the jet, which is located at point J, to point A on the coast of the island. He placed at stake in the sand at point A and recorded RA = 3.5 miles. Next, from point A he drove 6.4 miles to a tree at point T. He then proceeded along a straight path from the tree at point T in the direction of the jet to point B at which he planted another stake into the sand. He found that TB = 3.2 miles. In addition, he found RB = 7 miles and AB = 4.2 miles. Use the method below to find CJ, the distance between Master Chief and his target, the Covenant fighter jet. (Round displayed answers to the nearest tenth.) Will Master Chief be able to hit his target? Method: You can solve this problem by finding 7 measurements: (a) Find RAB . (b) Which angle is supplementary to RAB ? Find this angle. (c) Find TBA . (d) Find the angle which is supplementary to TBA . (e) At this point, you should know two angles in triangle ABJ . Find the missing angle. (f) Find AJ . (g) Find CJ . Hints: Use the following: The Law of Cosines Supplementary angles sum to 180 The Law of Sines Right triangle trigonometry J C T R A B 7. A triangle has an angle φ whose sine is equal to 1 2 . The angle is larger than 32 in measure. Find the exact measure (in degrees) of the angle φ . 8
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Lab 4 Math 148 - Spring 2012 Page 1 of 2 Answer Sheet – due Wednesday, May 30, 2012 Name: Recitation Time: 1. Solve 4 ABC if b = 14.1 , c = 11.8 , and C = 52.8 . How many solutions are there? (0, 1 or 2): angle A angle B side a First solution: Second solution: 2. Solve 4 ABC if A = 61.1 , C = 31.5 , and c = 10.9 . angle B side a side b Exactly one solution: 3. Solve 4 ABC if a = 39 , b = 35.6 , and c = 29.9 . angle A angle B angle C Exactly one solution: 4. Solve 4 ABC if B = 43.4 , a = 32.4 , and c = 30.9 . angle A angle C side b Exactly one solution: 5. (a) b = 30 , c = 47 , C = 52 Which method? Why? (b) B = 37 , c = 41 , C = 33 Which method? Why? (c) A = 54 , c = 29 , C = 90 Which method? Why? (d) a = 28 , b = 43 , c = 53 Which method? Why? (e) a = 42 , b = 45 , C = 161 Which method? Why? (f) a = 45 , A = 90 , b = 32 Which method? Why?
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