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Applications of Trigonometry and Vectors

Please see the attached file for the fully formatted problems.

1. Find the indicated part of each triangle ABC.
C = 118°, b = 130km, a = 75km; find c
The correct answer to this problem is 180 km how did they come up with that answer?

2. Height of a Balloon: The angles of elevation of a balloon from two points A and B on level ground are 24°50' and 47°20', respectively. As shown in the figure, points A, B, and C are in the same vertical plane and points A and B are 8.4 miles apart. Approximate the height of the balloon above the ground to the nearest tenth of a mile. The correct answer to this problem is 2.7 miles how did they come up with this answer?

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1.)
In triangle ABC, because,
cos(C) = (a^2 + b^2 - c^2)/(2*a*b)
=> cos(118) = (75^2 + 130^2 - c^2)/(2*75*130)
=> -0.469471563 = (22525 - c^2)/19500
=> 22525 - c^2 = ...

Solution Summary

Trigonometric application questions are solved. The solution is detailed and well presented. The solution received a rating of "5/5" from the student who originally posted the question.

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