Question

Solve for the missing length and the other two angles in the triangle below.



Part 1 - use law of cosines to find the missing 3rd side


Part 2- use either the law of cosines or the law of sines to find the measure of angle C


Part 3- Use any method you like to find the measure of angle B

Answer 1

The triangle is missing, so i have attached it.

Answer:

1) 3rd side = 12.92

2)angle C = 82°

3)angle B = 44°

Step-by-step explanation:

1) To find the missing 3rd side which is opposite to angle A, using cosine rule, we have

a² = b² + c² - 2bc•cosA

From the image,

b = 7.4 and c = 15.8 while A = 54°

Thus,plugging in relevant values ;

a² = 7.4² + 15.8² - 2(7.4*15.8)•cos54

a² = 54.76 + 249.64 - 137.45

a² = 166.95

a = √166.95

a ≈ 12.92

2) Using sine rule, we can find angle C.

Thus,

a/sinA = c/sinC

So, sin C = (c*sinA)/a

c = 15.8

a = 12.92

A = 54°

Plugging in the relevant values;

sin C = (15.8*sin54)/12.92

sin C = 0.98936

C = sin^(-1)0.98936

C ≈ 82°

3) to get angle B, we know that sum of angles in a triangle = 180.

Thus,

A + B + C = 180

So,54 + B + 82 = 180

B + 136 = 180

B = 180 - 136

B = 44°