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In triangle XYZ, if side XY is 8 cm, side YZ is 6 cm, and angle X is 45 degrees,

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Question: In triangle XYZ, if side XY is 8 cm, side YZ is 6 cm, and angle X is 45 degrees, which method can be used to find the length of side XZ?

Options:

  1. Pythagorean theorem
  2. Sine rule
  3. Cosine rule
  4. Area formula

Correct Answer: Cosine rule

Solution: 

To find the length of side XZ when two sides and the included angle are known, the Cosine rule is applicable.

In triangle XYZ, if side XY is 8 cm, side YZ is 6 cm, and angle X is 45 degrees,

Practice Questions

Q1
In triangle XYZ, if side XY is 8 cm, side YZ is 6 cm, and angle X is 45 degrees, which method can be used to find the length of side XZ?
  1. Pythagorean theorem
  2. Sine rule
  3. Cosine rule
  4. Area formula

Questions & Step-by-Step Solutions

In triangle XYZ, if side XY is 8 cm, side YZ is 6 cm, and angle X is 45 degrees, which method can be used to find the length of side XZ?
  • Step 1: Identify the sides and angle in triangle XYZ. We have side XY = 8 cm, side YZ = 6 cm, and angle X = 45 degrees.
  • Step 2: Recognize that we need to find the length of side XZ, which is opposite angle X.
  • Step 3: Since we have two sides (XY and YZ) and the included angle (X), we can use the Cosine rule.
  • Step 4: The Cosine rule formula is: c^2 = a^2 + b^2 - 2ab * cos(C), where a and b are the lengths of the sides, C is the included angle, and c is the side opposite the angle.
  • Step 5: In our case, let a = XY = 8 cm, b = YZ = 6 cm, and C = angle X = 45 degrees.
  • Step 6: Substitute the values into the Cosine rule formula to find the length of side XZ.
  • Cosine Rule – The Cosine Rule relates the lengths of the sides of a triangle to the cosine of one of its angles, allowing for the calculation of an unknown side when two sides and the included angle are known.
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