To solve for the side length $a$ in the given diagram, we can use trigonometric relationships. Here's the step-by-step process:

Step 1: Identify the relevant angles and sides.

From the diagram:

• $\alpha = 25.68^\circ$
• $\beta = 33.06^\circ$
• $b = 7.20$ cm

Step 2: Use the tangent function.

We can use the tangent function in relation to the angles $\alpha$ and $\beta$:

For $\alpha$: $\tan(\alpha) = \frac{b}{a}$ $\tan(25.68^\circ) = \frac{7.20 \text{ cm}}{a}$

Step 3: Solve for $a$.

First, calculate the value of $\tan(25.68^\circ)$: $\tan(25.68^\circ) \approx 0.4803$

Now, use the tangent function to solve for $a$: $a = \frac{7.20 \text{ cm}}{0.4803} \approx 14.99 \text{ cm}$

So, the side length $a$ is approximately $14.99$ cm.

Would you like more details or have any questions?

Related Questions:

1. How would you calculate side $b$ if $a$ and the angles were known?
2. How can you determine the length of the hypotenuse of the right triangle formed by $a$ and $b$?
3. What other trigonometric functions could be used to find $a$ or $b$?
4. How does changing $\alpha$ affect the side length $a$?
5. How would the solution change if angle $\alpha$ or $\beta$ was greater than $45^\circ$?

Tip:

Always double-check the angle units (degrees vs. radians) in your calculations to ensure accuracy.