3) A right-angled triangle is depicted. The lengths of the hypotenuse and one of the legs are given as 10 and 8 respectively. There is also a question mark next to the other leg, indicating it needs to be found. The right angle is clearly marked.

Problem Analysis:

• The image shows a right-angled triangle.
• The hypotenuse length is 10.
• One leg length is 8.
• The length of the other leg is unknown (marked with '?').

Solution:

We can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b):

\[ a^2 + b^2 = c^2 \]

Let 'a' be the unknown leg, 'b' be the known leg (8), and 'c' be the hypotenuse (10).

1. Substitute the known values into the Pythagorean theorem:

\[ a^2 + 8^2 = 10^2 \]

2. Calculate the squares:

\[ a^2 + 64 = 100 \]

3. Isolate a^2 by subtracting 64 from both sides:

\[ a^2 = 100 - 64 \]

\[ a^2 = 36 \]

4. Find 'a' by taking the square root of both sides:

\[ a = \sqrt{36} \]

\[ a = 6 \]

Final Answer:

The length of the unknown leg is 6.