To calculate the length $g$, we can use trigonometry in the isosceles triangle provided. Let’s analyze the problem step by step:

1. Given information:

   • Base of the triangle = $28.6 \, \text{cm}$.
   • Apex angle = $76^\circ$.
   • $g$ is the length of the two equal sides of the triangle.

2. Steps to solve:

   • The base is split into two equal halves ($28.6 / 2 = 14.3 \, \text{cm}$) by the height of the triangle.
   • In the right triangle formed, we use the cosine rule: $\cos(\text{angle}) = \frac{\text{adjacent}}{\text{hypotenuse}}$ Here:
     • Adjacent = $14.3 \, \text{cm}$,
     • Hypotenuse = $g$,
     • Angle = $76^\circ / 2 = 38^\circ$.

3. Cosine formula: $\cos(38^\circ) = \frac{14.3}{g}$ Rearranging for $g$: $g = \frac{14.3}{\cos(38^\circ)}$

4. Calculate $g$: Using a calculator: $g = \frac{14.3}{\cos(38^\circ)} \approx \frac{14.3}{0.7880} \approx 18.1 \, \text{cm}$

Final Answer:

The length $g$ is approximately 18.1 cm (to 1 decimal place).

Would you like further clarification or details on the trigonometric principles used?

Here are 5 related questions to deepen your understanding:

1. How does splitting the isosceles triangle simplify the calculation?
2. What would change if the apex angle was increased or decreased?
3. How can the sine or tangent rules be used here instead of cosine?
4. How can this method be generalized for other isosceles triangles?
5. What role does the unit (e.g., cm) play in these calculations?

Tip:

Always double-check angle splitting in isosceles triangles—it ensures symmetry and accurate calculations!