You present four different problems here (please present one at a time in the future). I'm going to assume that you want to focus on problem 2.
Your job is to solve this right triangle for x. Use the Pythagorean Theorem: a^2 + b^2 = c^2, where c is the length of the hypotenuse and a and b are the two side lengths.
Here, the two side lengths are x and 21, and the hypotenuse is 75.
According to the Pyth. Thm., x^2 + 21^2 = 75^2. After finding the two squares, we get x^2 + 441 = 5625.
Simplifying this, we get x^2 = 5184.
To find x, take the positive square root of both sides of this equation. Note: do not write the value of x as a decimal fraction. Instead, write "radical 5184" and then attempt to simplify this. Example: Does 5184 have a factor which is a perfect square? If so, write your final answer in the form "square root of that perfect square" times "square root of the remaining factor of 5184."
