How do you solve this oblique triangle using law of sines and cosines if angle B = 10degrees and 35 minutes, side a = 40 side c = 30?

1 Answer
Nghi N.
Jun 30, 2015

Solve oblique triangle

Ans: b = 12.17; A = 143.73; C = 25.92

Explanation:

Given: a = 40, c = 30, #B = 10^@35' = 10^@58#; cos 10^@58 = 0.98
Use trig identity: #b^2 = a^2 + c^2 - 2ac.cos B#

#b^2 = 1600 + 900 - 2400.cos B = 2500 - 2352 = 148#
b = 12.17.
Next, find A and C by the sine identity: #sin A/a = sin B/b.#

#sin A = (asin B)/b = (40(0.18))/12.17 = 7.19/12.17 = 0.59# -> #A = 36^@27# and #A = 180 - 36.27 = 143^@73.#.
This answer is accepted because the side a = 40 is the largest side.
Angle #C = 180 - A - B = 180 - 143.73 - 10.35 = 25^@92#

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