Knowing the lengths of the leg and hypotenuse, we determine the sines and cosines of the acute angles of the triangle.
CosН = КН / МН = 5/13.
Sin2H + Cos2H = 1.
Sin2H = 1 – (5/13) 2 = 1 – (25/169) = 144/169.
SinH = 12/13.
In a right-angled triangle, the sine of one acute angle is equal to the cosine of another acute angle, then:
SinM = CosH = 5/13.
SinH = CosM = 12/13.
Then tgM = SinM / CosM = (5/13) / (12/13) = 5/12,
tgH = SinH / CosH = (12/13) / (5/13) = 12/5.
Answer: SinM = CosH = 5/13, SinH = CosM = 12/13, tgM = 5/12, tgН = 12/5.
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