Triangle sides to angles

The triangle ABC has side lengths a = 14 cm, b = 20 cm, c = 7.5 cm. Find the sizes of the angles and the area of this triangle.

Correct answer:

S =  37.31 cm2
α =  29.8306 °
β =  134.7142 °
γ =  15.4552 °

Step-by-step explanation:

a=14 cm b=20 cm c=7.5 cm s=2a+b+c​=214+20+7.5​=483​=20.75 cm  S=s⋅ (s−a)⋅ (s−b)⋅ (s−c)​=20.75⋅ (20.75−14)⋅ (20.75−20)⋅ (20.75−7.5)​=37.31 cm2

Try calculation via our triangle calculator.

k=π180​=3.1416180​≐57.2958 α=k⋅ arccos(2⋅ c⋅ bb2+c2−a2​)=57.2958⋅ arccos(2⋅ 7.5⋅ 20202+7.52−142​)=29.8306∘=29°49′50"
β=k⋅ arccos(2⋅ a⋅ ca2−b2+c2​)=57.2958⋅ arccos(2⋅ 14⋅ 7.5142−202+7.52​)=134.7142∘=134°42′51"
γ=180−α−β=180−29.8306−134.7142=15.4552∘=15°27′19"

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