In a triangle mnk, the angle is k = 90 degrees mn = 13cm nk = 5 cm. Find the cos sin and tg of the angles m and n.

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.