Question

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?

Answer 1

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`