This is a right-angled triangle, and we are asked to calculate the value of $h$ (the hypotenuse) given that one of the angles is $35^\circ$ and the adjacent side (the base) has a length of 8 cm.

To calculate $h$, we can use trigonometric ratios. Specifically, the cosine function is appropriate here because we know the adjacent side and the angle:

$\cos(35^\circ) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{8}{h}$

Now, solve for $h$:

$h = \frac{8}{\cos(35^\circ)}$

Using a calculator to find $\cos(35^\circ)$:

$\cos(35^\circ) \approx 0.8192$

Thus:

$h = \frac{8}{0.8192} \approx 9.77 \, \text{cm}$

Therefore, the value of $h$ is approximately 9.77 cm.

Would you like any further details or have any additional questions about this solution?

Here are some related questions to explore:

1. How do you use the sine function to calculate the opposite side in right-angled triangles?
2. What happens if the angle in the triangle changes? How does that affect the hypotenuse length?
3. How can you calculate the area of this right-angled triangle using the base and height?
4. What is the relationship between trigonometric ratios and Pythagoras’ theorem?
5. How do you calculate the missing angle in a right-angled triangle if you know one side and the hypotenuse?

Tip: For trigonometric calculations, always make sure your calculator is set to the correct angle mode (degrees or radians) depending on the problem.