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

1 Answer

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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

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