Label the words of this 30,60,90 right triangle SL,2SL,and SLsqrt2 01510201131.png

Label the words of this 30,60,90 right triangle SL,2SL,and SLsqrt2 01510201131.png

Question
Label the words of this 30,60,90 right triangle \(\displaystyle{S}{L},{2}{S}{L},{\quad\text{and}\quad}{S}{L}\sqrt{{2}}\)
image

Answers (1)

2021-03-06
From the right triangle ABC, we have
\(\displaystyle\therefore{\sin{{\left({A}\right)}}}=\frac{{{B}{C}}}{{{A}{C}}}\)
\(\displaystyle\Rightarrow{\sin{{\left({30}^{\circ}\right)}}}=\frac{{v}}{{6}}\)
\(\displaystyle\Rightarrow{1}=\frac{{v}}{{3}}\)
\(\displaystyle\Rightarrow{v}={3}\)
From the right triangle ABC, we have
\(\displaystyle\therefore{\cos{{\left({A}\right)}}}=\frac{{{A}{B}}}{{{A}{C}}}\)
\(\displaystyle\Rightarrow{\cos{{\left({30}^{\circ}\right)}}}=\frac{{u}}{{6}}\)
\(\displaystyle\Rightarrow\frac{\sqrt{{3}}}{{2}}=\frac{{u}}{{6}}\)
\(\displaystyle\Rightarrow\sqrt{{3}}=\frac{{u}}{{3}}\)
\(\displaystyle\Rightarrow{u}={3}\sqrt{{3}}\)
Since, the sum of all angles of a triangle is \(\displaystyle{180}^{\circ}\)
\(\displaystyle\therefore\angle{A}+\angle{B}+\angle{C}={180}^{\circ}\)
\(\displaystyle\Rightarrow{30}^{\circ}+{90}^{\circ}+\angle{C}={180}^{\circ}\)
\(\displaystyle\Rightarrow{120}^{\circ}+\angle{C}={180}^{\circ}\)
\(\displaystyle\Rightarrow\angle{C}={60}^{\circ}\)
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