Answer:

To solve for the missing side of a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. That is:

c^2 = a^2 + b^2

where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

Using this formula, we can solve for the missing side in each case:

a=8 and c=17, find b:

c^2 = a^2 + b^2

17^2 = 8^2 + b^2

289 = 64 + b^2

225 = b^2

b = √225

b = 15

Therefore, the missing side b has a length of 15 units.

b=12 and c=20, find a:

c^2 = a^2 + b^2

20^2 = a^2 + 12^2

400 = a^2 + 144

256 = a^2

a = √256

a = 16

Therefore, the missing side a has a length of 16 units.

a=14 and b=6, find c:

c^2 = a^2 + b^2

c^2 = 14^2 + 6^2

c^2 = 196 + 36

c^2 = 232

c = √232

We can simplify √232 by breaking it down into a product of its prime factors:

√232 = √(2^3 × 29) = 2√29√

Therefore, the missing side c has a length of 2√29 units.

Answer:

1.a=8 and c=17 find b

2.b=12 and c=20 find a