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?
Pythagorean theorem
Sine rule
Cosine rule
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.
