Solve the triangle. A = 21°, C = 105°, c = 5

Answer 1

Solve the traingle by using AAS rule

The traingle measurements are A = 21° , C = 105° and one side c = 5.

To solve the triangle we need to solve remaining angle B and side a and b.

We know Sum of angles in traingle = 180°

Therfore angle B = 180 -(21 + 105)

B = 54°

Use law of sines sinA/a = sinC/c = sinB/b

sinA/a = sinC/c

sin(21)/a = sin(105)/5

a = [5sin(21)]/sin(105)

a = [5(0.358)]/0.965

a = 1.79/0.965

a = 1.854

Now sinC/c = sinB/b

sin(105)/5 = sin(54)/b

b = 5sin(54)/sin(105)

b = 5(0.809)/0.965

b = 4.045/0.965

b = 1.036.

Therefore, a = 1.854, b = 1.036 and B = 54°.