To solve for the length of side $a$ in the right triangle, we use the Pythagorean theorem:

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

Here:

• $b = 17$,
• $c = 20$ (the hypotenuse).

Substituting the known values:

$a^2 + 17^2 = 20^2$

$a^2 + 289 = 400$

$a^2 = 400 - 289$

$a^2 = 111$

Taking the square root of both sides:

$a = \sqrt{111} \approx 10.5$

The length of side $a$ is approximately 10.5 (rounded to one decimal place).

Would you like additional explanations or details?

Related Questions:

1. How does the Pythagorean theorem apply to other types of triangles?
2. What are some methods to approximate square roots if a calculator is unavailable?
3. How can you determine if a triangle is a right triangle given its side lengths?
4. What are practical applications of the Pythagorean theorem in real-life scenarios?
5. What happens if the triangle's hypotenuse length is unknown—how would you find it?

Tip:

Always double-check your calculations, especially when using square roots, to ensure precision!