Let's solve the two right triangles shown in the image using the Pythagorean theorem, which states that for a right triangle:

$a^2 + b^2 = c^2$ where $a$ and $b$ are the legs, and $c$ is the hypotenuse.

Part (a):

In triangle (a), we are given:

• One leg: $a = 2.5$ inches
• The hypotenuse: $c = 6.5$ inches

We need to find the other leg, $b$.

Using the Pythagorean theorem: $a^2 + b^2 = c^2$ $(2.5)^2 + b^2 = (6.5)^2$ $6.25 + b^2 = 42.25$ $b^2 = 42.25 - 6.25 = 36$ $b = \sqrt{36} = 6 \text{ inches}$

So, the missing side for triangle (a) is 6.000 inches.

Part (b):

In triangle (b), we are given:

• One leg: $a = 7.61$ feet
• The other leg: $b = 15.18$ feet

We need to find the hypotenuse, $c$.

Using the Pythagorean theorem: $a^2 + b^2 = c^2$ $(7.61)^2 + (15.18)^2 = c^2$ $57.9121 + 230.8324 = c^2$ $c^2 = 288.7445$ $c = \sqrt{288.7445} \approx 16.993 \text{ feet}$

So, the hypotenuse for triangle (b) is approximately 16.993 feet.

Would you like more details or have any questions?

Here are some related questions for further practice:

1. How do you calculate the hypotenuse when both legs are given?
2. What is the Pythagorean theorem and how is it used in right triangles?
3. How do you determine if a triangle is a right triangle given three sides?
4. Can the Pythagorean theorem be applied to non-right triangles?
5. What are some practical uses of the Pythagorean theorem in real life?

Tip: Always check whether a triangle is a right triangle before using the Pythagorean theorem.