missing parts

Question

FInd the missing parts of the triangle

 

B= 12.6 degrees

b- 15.74

a= 17.35

Answer 1

Use the Law of Sines to determine A

 

sin A / a = sin B / b

sin A / 17.35 = sin 12.6 / 15.74

 

After determining A, determine C (180 - A - B)

 

Use the Law of Sines again

 

c / sin C = 15.74 / sin 12.6

Answer 2

First step: Since we are given two known sides and one known angle, we can use law of sines to find angle A.

 

(SinB / b) = (SinA / a)

 

Cross multiply, we obtain

 

bSinA = aSinB

 

15.74*SinA = 17.35*Sin(12.6)

 

SinA = [17.35*Sin(12.6)] / 15.74

 

SinA = 0.240

 

A = Sin^-1(0.240)

 

A = 13.89 degrees

 

 

Second step: Now that we have two know angles, we can find the missing angle C by adding those angles and subtracting the sum from 180.

 

C = 180 - (A + B)

C = 180 - (13.89 + 12.60)

C = 153.51 degrees

 

 

Third step: Now that we have all three angles of the triangle and two known sides, we can now use law of cosines to find the missing side c.

 

c² = a² + b² - 2abCosC

 

c² = a² + b² - 2abCosC

 

c² = (17.35)² + (15.74)² - 2(17.35)(15.74)(Cos153.51)

 

c² = 1037.61

 

c = √(1037.61)

 

c = 32.21