Question

Find the angle B in an oblique triangle in which a = 31, b = 15, and c = 17. A. 13º28' B. 15º19' C. 151º13' D. 148º47'

Answer 1

We can find the measure of angle B using the Law of cosines.

According to the Law of Cosines:

$b^{2} = a^{2} + c^{2} - 2ac*cos(B) \\ \\ 2ac*cos(B)= a^{2} + c^{2}- b^{2} \\ \\ cos(B)= \frac{a^{2} + c^{2}- b^{2}}{2ac}$

Using the values of a,b and c in the above equation we get:

$cos(B)= \frac{31^{2}+17^{2}-15^{2}}{2*31*17} \\ \\ cos(B)= \frac{1025}{1054} \\ \\ B=cos^{-1}(\frac{1025}{1054}) \\ \\ B=13.47$

Thus measure of angle B is 13.47 degrees. We can convert the decimal part to minutes by multiplying it by 60.

So measure of angle B will be 13 degrees and (60 x 0.47) minutes which equals 13 degrees and 28 minutes or 13° 28'.

Thus option A gives the correct answer.

Answer 2

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