The leg and the hypotenuse are 6 cm and 10 cm, respectively. Find the sine and tangent of the acute angle opposite the given leg.

leg (let it be a) = 6 cm.
hypotenuse (let it be c) = 10 cm.
Sinus is the ratio of the opposite leg to the hypotenuse.
1) sin = a / c = 6/10 = 3/5
Tangent is the ratio of the opposite leg to the adjacent leg.
1) by the Pythagorean theorem, we are looking for the second leg (let it be b):
b ^ 2 = 10 ^ 2-6 ^ 2 = 100-36 = 64
b = 8
2) tg = a / b = 6/8 = 3/4