To solve this problem, we can use the Pythagorean theorem, which states:

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

Here:

• $c$ is the hypotenuse (16 in this case),
• $a$ is the given leg (4),
• $b$ is the unknown leg labeled $l$.

Step 1: Write the equation

$4^2 + l^2 = 16^2$

Step 2: Simplify the known values

$16 + l^2 = 256$

Step 3: Isolate $l^2$

$l^2 = 256 - 16$ $l^2 = 240$

Step 4: Solve for $l$

$l = \sqrt{240}$

Using a calculator: $l \approx 15.5$

Final Answer:

The length of the leg labeled $l$ is approximately 15.5 (to 1 decimal place).

Would you like a detailed explanation of any step or further help?

Here are 5 related questions for practice:

1. What is the length of a triangle's leg if the hypotenuse is 20 and the other leg is 12?
2. How can the Pythagorean theorem be used in 3D space?
3. What happens if all sides of the triangle are integers, such as 3-4-5?
4. How do you determine if a triangle is a right triangle given the sides?
5. Can you apply the Pythagorean theorem to non-right triangles?

Tip: Always double-check which side is the hypotenuse; it’s the longest side and opposite the right angle!