To solve for the third side of the right triangle, we can apply the Pythagorean theorem, as it involves a right angle.

The Pythagorean theorem states: $a^2 + b^2 = c^2$ where $a$ and $b$ are the lengths of the two legs, and $c$ is the length of the hypotenuse (the side opposite the right angle).

From the image:

• One leg is 18 units.
• The other leg is 30 units.

Now, we can plug these values into the Pythagorean theorem to find the length of the third side:

$a^2 + b^2 = c^2$ $18^2 + 30^2 = c^2$ $324 + 900 = c^2$ $1224 = c^2$ $c = \sqrt{1224}$ Now, we calculate $c$. math

Calculate the hypotenuse

c = math.sqrt(1224) cThe length of the third side (the hypotenuse) is approximately 35.0 units when rounded to the nearest tenth.

Would you like further clarification or additional details? Here are some related questions you may find useful:

1. How do you apply the Pythagorean theorem to non-right triangles?
2. What is the relationship between the sides of a 45-45-90 triangle?
3. How can you use trigonometry to find the sides of a right triangle?
4. How do you solve for missing sides using the law of sines or cosines?
5. What is the importance of the Pythagorean theorem in real-world applications?

Tip: Always double-check the units and whether the triangle is a right triangle before applying the Pythagorean theorem.