This image shows a right triangle, with a perpendicular height of 7 cm, a slant height (hypotenuse) of 9 cm, and the base labeled as $x$ cm. Additionally, there is an angle $\theta$ on the right side of the triangle.

To solve for $x$, we can use the Pythagorean theorem, which states:

$c^2 = a^2 + b^2$

Where:

• $c$ is the hypotenuse (9 cm),
• $a$ is the height (7 cm),
• $b$ is the base ($x$).

Let's calculate $x$ using this formula.

$9^2 = 7^2 + x^2$

$81 = 49 + x^2$

$x^2 = 81 - 49$

$x^2 = 32$

$x = \sqrt{32} \approx 5.66 \, \text{cm}$

So, $x \approx 5.66 \, \text{cm}$.

Would you like further details or have any questions?

Here are 5 related questions:

1. How can we calculate the area of this triangle?
2. What is the value of $\theta$ using trigonometry?
3. How do we find the perimeter of this triangle?
4. What other methods can be used to solve for $x$?
5. What is the significance of the right angle in the triangle's properties?

Tip: In any right triangle, the Pythagorean theorem is a powerful tool for solving for unknown sides when two sides are given.