Circumscribed circle

In triangle ABC, we know a = 4 cm, b = 6 cm, γ = 60°. Calculate the area and radius of the inscribed and circumscribed circle.

Final Answer:

S =  10.3923 cm2
r =  1.3592 cm
R =  3.0551 cm

Step-by-step explanation:

a=4 cm b=6 cm γ=60 ∘  c2 = a2+b2 − 2ab⋅ cos γ  c=a2+b2−2⋅ a⋅ b⋅ cosγ​=a2+b2−2⋅ a⋅ b⋅ cos60° ​=42+62−2⋅ 4⋅ 6⋅ cos60° ​=42+62−2⋅ 4⋅ 6⋅ 0.5​=5.2915 cm  s=2a+b+c​=24+6+5.2915​≐7.6458 cm  S=s⋅ (s−a)⋅ (s−b)⋅ (s−c)​=7.6458⋅ (7.6458−4)⋅ (7.6458−6)⋅ (7.6458−5.2915)​=6 3​ cm cm=10.3923 cm2
S=r⋅ s  r=S/s=10.3923/7.6458=1.3592 cm

Try calculation via our triangle calculator.

R=4⋅ r⋅ sa⋅ b⋅ c​=4⋅ 1.3592⋅ 7.64584⋅ 6⋅ 5.2915​=3.0551 cm

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arithmeticplanimetricsgoniometry and trigonometryUnits of physical quantitiesGrade of the word problem

 
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