Triangle

Calculate the area of ​​the triangle ABC if b = c = 17 cm, R = 19 cm (R is the circumradius).

Result

S =  115.63 cm2

Solution:

cos⁡α2=c/2r α=2arccos⁡c/2r=126∘51′ β=γ=180∘−α2=27∘  S=2r2sin⁡αsin⁡βsin⁡γ=115.63 cm2\cos \dfrac{\alpha}{2} = \dfrac{c/2}{r} \ \\ \alpha = 2 \arccos \dfrac{c/2}{r} = 126^\circ 51' \ \\ \beta = \gamma = \dfrac{ 180 ^\circ - \alpha }{2} = 27^\circ \ \\ \ \\ S = 2r^2 \sin \alpha \sin \beta \sin \gamma = 115.63 \ \text{cm}^2

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