https://file.aiquickdraw.com/mathbot/file/1739210120311lhvhwntz.jpg

To determine the largest angle in triangle XYZ, we need to use the triangle's side lengths. The side lengths are:

- XY = 8.5 cm
- YZ = 7.2 cm
- XZ = 6.3 cm

The largest angle is opposite the longest side, so it will be opposite side XY (8.5 cm). To calculate this angle, we can use the **Cosine Rule**:

\[
\cos C = \frac{a^2 + b^2 - c^2}{2ab}
\]

Where:
- \( a \) and \( b \) are the other two sides (YZ = 7.2 cm, XZ = 6.3 cm),
- \( c \) is the longest side (XY = 8.5 cm).

We can now substitute the values into the formula and solve for the angle. math

# Given side lengths
a = 7.2  # YZ
b = 6.3  # XZ
c = 8.5  # XY

# Applying the cosine rule to find angle C (largest angle)
cos_angle_C = (a**2 + b**2 - c**2) / (2 * a * b)

# Calculating angle C in degrees
angle_C = math.acos(cos_angle_C) * (180 / math.pi)
angle_CThe largest angle in triangle XYZ, which is opposite the longest side (XY = 8.5 cm), is approximately **77.73°**.

Would you like further details or have any other questions on this? 

Here are some related questions for further exploration:
1. How does the cosine rule work for finding angles in triangles?
2. What is the difference between the sine, cosine, and tangent rules in trigonometry?
3. How do we find the other angles in a triangle once we have one angle?
4. Can the cosine rule be used for non-right-angled triangles?
5. What is the importance of the longest side in determining the largest angle?

Tip: Always check which side corresponds to the angle you are trying to calculate in the triangle; this helps in applying the correct formula.

Calculate the size of the largest angle in the triangle XYZ.

Learn how to determine the largest angle in triangle XYZ with side lengths 6.3 cm, 7.2 cm, and 8.5 cm using the Cosine Rule. Step-by-step calculations included. Suitable for students in Grades 9-12.

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