Rectangular triangle KLM with right angle at vertex L, angle beta at vertex K, and angle alpha at vertex M. Angle at vertex M = 65°, side l = 17.5 cm. Use Pythagorean theorems and trigonometric functions to calculate the lengths of all sides and the angle at the vertex K.

Correct answer:

m =  15.8604 cm
K =  25 °
k =  7.3958 cm

Step-by-step explanation:

L=90  M=65  l=17.5 cm  sin M = m:l  m=l sinM=l sin65° =17.5 sin65° =17.5 0.906308=15.86=15.8604 cm
K+L+M=180°  K=180LM=1809065=25
sin K = k:l  k=l sinK=l sin25° =17.5 sin25° =17.5 0.422618=7.396=7.3958 cm

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