Solve-the-triangle-in-which-a-3-1-b-3-1-and-C-60-

Question Number 18904 by Satyamtt last updated on 01/Aug/17

S o l v e t h e t r i a n g l e i n w h i c h a = (\sqrt{3} + 1),

b = (\sqrt{3} - 1) a n d ∠ C = 60 ° .

Answered by behi.8.3.4.1.7@gmail.com last updated on 01/Aug/17

c^{2} = a^{2} + b^{2} - 2 a b . c o s C =

= {(\sqrt{3} + 1)}^{2} + {(\sqrt{3} - 1)}^{2} - 2 . (\sqrt{3} - 1) (\sqrt{3} + 1) . \frac{1}{2} =

= 8 - 2 = 6 \Rightarrow c = \sqrt{6}

\frac{a}{s i n A} = \frac{c}{s i n C} \Rightarrow s i n A = \frac{\sqrt{3} + 1}{\sqrt{6}} . \frac{\sqrt{3}}{2} = \frac{3 + \sqrt{3}}{2 \sqrt{6}} =

= \frac{3 \sqrt{6} + 3 \sqrt{2}}{12} = \frac{\sqrt{6} + \sqrt{2}}{4} \Rightarrow A = 75^{∙}

B = 180 - (60 + 75) = 45^{∙}