To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse ($c$) is equal to the sum of the squares of the other two legs ($a$ and $b$):

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

In this triangle:

• The hypotenuse is the longest side, which is given as $7 \, \text{cm}$.
• One leg is given as $2 \, \text{cm}$.
• The other leg, $b$, is the unknown we need to find.

Step-by-Step Solution

1. Set up the equation using the Pythagorean theorem: $7^2 = 2^2 + b^2$

2. Substitute the values and simplify: $49 = 4 + b^2$

3. Isolate $b^2$ by subtracting 4 from both sides: $b^2 = 49 - 4$ $b^2 = 45$

4. Solve for $b$ by taking the square root of both sides: $b = \sqrt{45}$ $b \approx 6.7$

Final Answer

The length of the missing leg $b$ is approximately 6.7 cm, rounded to the nearest tenth.

Would you like more details, or do you have any questions?

Here are five related questions to expand on this topic:

1. How would the answer change if the given leg was 3 cm instead of 2 cm?
2. Can you calculate the area of this triangle with the given and found side lengths?
3. How does the Pythagorean theorem apply to non-right triangles?
4. What is the relationship between the sides in a 45°-45°-90° triangle?
5. How can we use trigonometry to solve for unknown sides in a right triangle?

Tip: Remember, the Pythagorean theorem only applies to right triangles.