Find the unknown sides and acute angles of a right-angled triangle if the leg is 20 and the hypotenuse is 29.

To solve this problem, recall the Pythagorean theorem. According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the legs. Knowing that the hypotenuse is 29 cm, and the leg is 20 cm, we calculate the length of the second leg -x.
x ^ 2 = 29 ^ 2-20 ^ 2 = 841-400 = 441;
x ^ 2 = 441;
x = √441 = 21 cm.
To find the acute angles of a right-angled triangle, calculate the sine of the angle. Recall that the sine of the angle is equal to the ratio of the opposite leg to the hypotenuse.
sine x = 21/29 = 0.7241.
Calculate the degree from the sine table.
Sine x = 0.7241 = 46, 40 degrees.
Let’s calculate the third angle.
180-90-46.4 = 43.6 degrees.
Answer: 46.4 degrees, 43.6 degrees.