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To solve for the size of angle \(\theta\) in the isosceles triangle, we can use trigonometry and the fact that it's an isosceles triangle.

We know the following:
- Two equal sides are 9.6 cm.
- The base is 6.8 cm.

Since it's an isosceles triangle, we can split the triangle into two right-angled triangles, each with:
- One leg of half the base, which is \( \frac{6.8}{2} = 3.4 \, \text{cm} \).
- Hypotenuse of 9.6 cm.
- The angle adjacent to the base will be \( \frac{\theta}{2} \), where \(\theta\) is the full angle at the top.

We can use the cosine rule (for right triangles):
\[
\cos \left( \frac{\theta}{2} \right) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{3.4}{9.6}
\]

Let's calculate \(\theta\).

The size of angle \(\theta\) in the isosceles triangle is \(138.5^\circ\), rounded to one decimal place.

Would you like further details or have any questions? Here are some related questions to deepen your understanding:

1. What is the sum of the angles in any triangle?
2. How does the Pythagorean theorem apply to right-angled triangles?
3. Can you explain the difference between sine, cosine, and tangent in trigonometry?
4. How would the calculation change if the base were different?
5. What other methods can be used to solve for unknown angles in isosceles triangles?

**Tip:** For isosceles triangles, always remember that the two equal sides form equal angles with the base!

Calculate the size of angle θ in the isosceles triangle with sides of 9.6 cm and a base of 6.8 cm.

Learn how to calculate the size of angle θ in an isosceles triangle with sides of 9.6 cm and a base of 6.8 cm using trigonometry and the cosine rule. This problem is perfect for students in Grades 9-11 and covers key trigonometric concepts.

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