Cosine

Cosine and sine theorem:
Calculate all unknown 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+b2−2⋅ a⋅ b⋅ cosγ​=a2+b2−2⋅ a⋅ b⋅ cos90° ​=202+152−2⋅ 20⋅ 15⋅ cos90° ​=202+152−2⋅ 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°7′48"
sin β : sin γ = b:c β=π180°​⋅arcsin(cb​⋅ sin(π/2))=π180°​⋅arcsin(2515​⋅ sin(3.1416/2))=36.8699∘=36°52′12"

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