Calculate 3209

Calculate the lengths of the sides of the triangle ABC, in which angles α = 113°, β = 48°, and the radius of the circle of the triangle described is r = 10 cm.

Correct answer:

a =  18.4101 cm
b =  14.8629 cm
c =  6.5114 cm

Step-by-step explanation:

$$\begin{gathered} R=10 \\ A=113 \\ B=48 \\ C=180-A-B=180-113-48=19 \\ a=2\cdot R\cdot \sin A=2\cdot R\cdot \sin 113°=2\cdot 10\cdot \sin 113°=2\cdot 10\cdot 0.920505=18.41=18.4101\text{cm} \end{gathered}$$

$b=2\cdot R\cdot \sin B=2\cdot R\cdot \sin 48°=2\cdot 10\cdot \sin 48°=2\cdot 10\cdot 0.743145=14.863=14.8629\text{cm}$

$c=2\cdot R\cdot \sin C=2\cdot R\cdot \sin 19°=2\cdot 10\cdot \sin 19°=2\cdot 10\cdot 0.325568=6.511=6.5114\text{cm}$

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