Answer:
The length of x is 155 cm to the nearest centimeter
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