First find x from the Pythagorean theorem a^2 + b^2 = c^2, where c is the hypotenuse.
7^2 + 24^2 = c^2
49 + 576 = c^2
c^2 = 625, so c = 25
Then to figure out y and z you need to use inverse trigonometric functions.
Use arctan(7/24) = y = 16.3 degrees and arctan(24/7) = z = 73.7 degrees.