Evaluate (frac{2sin 30 + 5tan 60}{sin 60}), leaving your answer in surd form.
-
A.
(frac{2sqrt{3}}{3} + 10) -
B.
(frac{3sqrt{2} – 1}{5}) -
C.
(frac{3sqrt{2} + 1}{5}) -
D.
(frac{2sqrt{3}}{3} – 10)
Correct Answer: Option A
Explanation
(frac{2sin 30 + 5tan 60}{sin 60})
(sin 30 = frac{1}{2}; tan 60 = sqrt{3}; sin 60 = frac{sqrt{3}}{2})
(therefore frac{2sin 30 + 5tan 60}{sin 60} = frac{2(frac{1}{2}) + 5(sqrt{3})}{frac{sqrt{3}}{2}}))
= (frac{1 + 5sqrt{3}}{frac{sqrt{3}}{2}})
= (frac{2(1 + 5sqrt{3})}{sqrt{3}})
= (frac{2 + 10sqrt{3}}{sqrt{3}})
Rationalizing, we get
= (frac{2sqrt{3} + 30}{3})
= (frac{2}{3} sqrt{3} + 10)
There is an explanation video available below.