.solve the triangle?

Question

Angle C = 96 degrees

Angle A and B = Unknown

a = 6

b = 4

c = unknown 

Answer 1

When two sides are given and an included angle (an angle between the two given sides). Your only choice is to use Cosine Law:

 

c² = a² + b² -2abCosC (Remember, the a, b and c here are now fixed, it depends on which 2 given sides are given and which included angle)

 

Using the equation:

 

c² = 6² + 4² -2(6)(4)cos96

 

c² = 57.0174

 

c = 7.551

 

From here, it's better to use Sine Law to get the remaining angles:

 

(sinA)/a = (sinB)/b = (sinC)/c

 

Let's use (sinA)/a = (sinC)/c

 

(sinA)/6 = (sin96)/7.551

 

sinA = 0.7902

 

A = Sin^-10.7902 = 52.208º

 

To get B, either repeat the process above, using (sinB)/b or you could just add the three angles with the sum of 180.

 

A + B + C = 180

52.208 + B + 96 = 180

 

B = 31.792º