FIND THE MISSING SIDE AND ANGLE OF A TRIANGLE USING COSINE RULE

The cosine law can be used which is not a right triangle.

a² = b² + c² - 2bc cos A

b² = c² + a² - 2ac cos B

c² = a² + b² - 2ab cos C

Problem 1 :

Solution:

By using cosine rule,

a² = b² + c² - 2bc cos(A)

x² = 17² + 17² - 2(17)(17) cos(70°)

x² = 289 + 289 - 578(0.34)

x² = 381.48

x = √381.48

x = 19.53 cm

Problem 2 :

Solution:

By using cosine rule,

a² = b² + c² - 2bc cos(A)

x² = (6.1)² + (5.5)² - 2(6.1)(5.5) cos(148°)

x² = 37.21 + 30.25 - 67.1(-0.848)

x² = 67.46 + 56.9

x² = 124.36

x = √124.36

x = 11.15 cm

Problem 3 :

Solution:

By using cosine rule,

a² = b² + c² - 2bc cos(A)

x² = 6² + 7² - 2(6)(7) cos(19°)

x² = 36 + 49 - 84(0.945)

x² = 85 - 79.38

x² = 5.62

x = √5.62

x = 2.37 cm

Problem 4 :

Solution:

By using cosine rule,

Problem 5 :

Solution:

By using cosine rule,

Problem 6 :

Solution:

By using cosine rule,