Question 24

ΔDEF is right angled at E. If m$$\angle$$D = $$30^\circ$$, then find the value of $$(\cos F + \sqrt3)$$

Solution

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

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

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

To find : $$(\cos F + \sqrt3)$$

= $$cos(60^\circ)+\sqrt3$$

= $$\frac{1}{2}+\sqrt3$$

= $$\frac{(1+2\sqrt3)}{2}$$

=> Ans - (B)


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