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Find the area of the triangle whose two angles are 30 degrees and 45 degrees, and the side included between them has sqrt(3) + 1 length units.

 Jul 3, 2021
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Find the area of the triangle whose two angles are 30 degrees and 45 degrees, and the side included between them has sqrt(3) + 1 length units.

 

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\(tan(30°)=\frac{h}{\sqrt{3}+1-h}\\ \frac{ \sqrt{3} }{3} (\sqrt{3}+1-h)=h\\ 1+\frac{ \sqrt{3} }{3}-\frac{ h\sqrt{3} }{3}=h\\ 1+\frac{ \sqrt{3} }{3}=h+\frac{ h\sqrt{3} }{3}\\ 1+\frac{ \sqrt{3} }{3}=h(1+\frac{ \sqrt{3} }{3}) \)

\(h=1\)

\(A=\frac{h}{2}(\sqrt{3}+1)\\ A=\frac{1}{2}(\sqrt{3}+1)\\ A= \color{blue}\frac{\sqrt{3}}{2}+\frac{1}{2}=1.3660\)

laugh  !

 Jul 4, 2021

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