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Q.
The circular measures of two angles of a triangle are $\frac{1}{2}$ and $\frac{1}{3}$, find the third angle in English system.
Trigonometric Functions
Solution:
We know that the sum of three angles of a triangle is $180^{\circ}$, i.e., $\pi$ radians
$\therefore $ The third angle $=\left(\pi-\frac{1}{2}-\frac{1}{3}\right)$ radian
$\simeq\left(\frac{22}{7}-\frac{1}{2}-\frac{1}{3}\right)^{c}=\left(\frac{97}{42}\times\frac{180}{\pi}\right)^{\circ}\,\left(\because \pi^{c}=180^{\circ}\right)$
$=\left(\frac{97 \times 30}{22}\right)^{\circ}=\frac{1455}{11}$ degree
$=\left(132 \frac{3}{11}\right)^{\circ}$
$=132^{\circ}\left(\frac{3 \times 60}{11}\right)'$ $\,\left(\because 1^{\circ}=60'\right)$
$=132^{\circ}\left(16+\frac{4}{11}\right)'$
$=132^{\circ}16'\left(\frac{4}{11}\times 60\right)''\,\left(\because 1'=60'\right)$
$=132^{\circ}\,16'\,22''$.