Question 24

∆DEF is right angled at E. If m$$\angle$$F = $$30^\circ$$, then find the value of $$(sin D - \frac{1}{3})$$.

Solution

Sum of angles of $$\triangle$$ DEF = $$\angle D+\angle E+\angle F=180^\circ$$

=> $$\angle D+90^\circ+30^\circ=180^\circ$$

=> $$\angle D=180^\circ-120^\circ=60^\circ$$

To find : $$(sin D - \frac{1}{3})$$

= $$sin(60^\circ)-\frac{1}{3}$$

= $$\frac{\sqrt3}{2}-\frac{1}{3}$$

= $$\frac{(3\sqrt3-2)}{6}$$

=> Ans - (B)

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