In ΔXYZ, y = 75 cm, z = 83 cm and ∠X=157°. Find the length of x, to the nearest centimeter.

The length of x is 155 cm to the nearest centimeter

Step-by-step explanation:

To solve a triangle we use the sine rule or cosine rule

In the triangle XYZ

∵ y is opposite to ∠Y

∵ x is opposite to ∠X

∵ z is opposite to ∠Z

∵ y = 75 cm and z = 83 cm

∵ m∠X = 157°

→ We have 2 sides and the included angle, then use the cosine rule

∴ x² = y² + z² - 2yz cos X

→ Substitute the given values in the rule

∵ x² = (75)² + (83)² - 2(75)(83) cos(157°)

∴ x² = 23974.28543

→ Take a √  for both sides

∴ x = 154.8363182

→ Round it to the nearest cm (nearest whole number)

∴ x = 155 cm

∴ The length of x is 155 cm to the nearest centimeter