MathTrigonometry
posted by Duane on .
Master Chief is trapped on an island with a Scorpion Tank as his only means of defense.
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 4.5 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 = 3.7 miles. Next, from point A he drove 6.8 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 = 3.5 miles. In addition, he found RB = 6.6 miles and AB = 4.3 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

He'd definitely be able to blow it up. He drove his tank *right up to it*, after all.
However, he wouldn't want to destroy it as it's his only way off the island...
(Protip: When writing questions, make sure that the physical elements match what you're actually trying to calculate!)