Suppose that: hypotenuse AB = 41 cm, leg BC = 40 cm.Applying the Pythagorean theorem, we find the length of the other leg:
AB ^ 2 = BC ^ 2 + AC ^ 2;
AC ^ 2 = AB ^ 2 – BC ^ 2;
AC ^ 2 = 41 ^ 2 – 40 ^ 2 = 1681 – 1600 = 81;
AC = √81 = 9 cm.
The smaller acute angle of this triangle will be the angle ∠B, since it is it that lies opposite the larger leg.
The sinus is the ratio of the opposite leg to the hypotenuse:
sin B = AC / AB;
sin B = 9/41 = 0.2195.
Cosine is the ratio of the adjacent leg to the hypotenuse:
cos B = BC / AC;
cos B = 40/41 = 0.9756.
Tangent – the ratio of the opposite leg to the adjacent one:
tg B = AC / BC;
tg B = 9/40 = 0.225.
Answer: sin B = 0.2195; cos B = 0.9756; tg B = 0.225.
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