Solve the triangle if possible. determine the number of possible solutions.

Question

A=76.2° a=12.4 b=9.2

Photo Link: https://ibb.co/tDk5zt7

Answer 1

Hello!

So here we have a triangle with sides a, b, c and angles A,B,C

Something to note: Sine rule: a/sinA=b/sinB=c/sinC

Find B:

a/sinA=b/sinB.

sinB=bsinA/a (solve for angle B)

sinB=(9.2)sin(76.2)/(12.4)

B= 46.1°

Find C:

Triangle is 180°

A+B+C=180°

180°-A-B=C

180°-76.2°-46.1°=57.7°

C=57.7°

Find c:

using ratio of side to sine angle:

a/sinA=c/sinC

c=sinCa/sinA (algebra)

c=sin(57.7)(12.4)/sin(76.2)

c=10.8

Hope this helps!