Cosine and sine theorem:
Calculate all missing values (sides and angles) of the triangle ABC.

a = 20 cm; b = 15 cm; γ = 90°; c =? cm; α =? °; β =? °

Correct answer:

c =  25 cm
α =  53.1301 °
β =  36.8699 °

Step-by-step explanation:

a=20 cm b=15 cm γ=90   c2 = a2+b2  2 a b cos γ  c=a2+b22 a b cosγ=a2+b22 a b cos90° =202+1522 20 15 cos90° =202+1522 20 15 0=25=25 cm   Verifying Solution:  c2=a2+b2=202+152=25 cm  cos 90° = cos π/2 = 0 sin 90° = sin π/2 = 1
sin α : sin γ = a:c α=π180°arcsin(ca sin(π/2))=π180°arcsin(2520 sin(3.1416/2))=53.1301=53°748"
sin β : sin γ = b:c β=π180°arcsin(cb sin(π/2))=π180°arcsin(2515 sin(3.1416/2))=36.8699=36°5212"

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