Find the hypotenuse and acute angles of a right-angled triangle along the legs a = 5 dm. and b = 10dm.

By the Pythagorean theorem:
c² = a² + b²; a = 5 dm; b = 10 dm;
c² = 25 + 100 = 125 (dm²); c = √125 = √ (25 * 5) = 5 √5 (dm);
Angles A and B are acute angles of the triangle.
The tangent of the angle is equal to the ratio of the opposite leg to the adjacent one.
tg <A = a: b = 5: 10 = 0.5; <A = 27 °;
<A + <B = 90 °; <B = 90 ° – 27 ° = 63 °.