Question

If △ABC is a right triangle with ∠ACB=90∘ and ∠BAC=30∘ and AB=6 . What is the length of AC?
(A) 3√3
(B) 2√3
(C) 3√2
(D) 3/2

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{In\;\triangle\;ABC,\;\angle{ACB}=90^\circ,\angle{BAC}=30^\circ\;and\;AB=6}$

$\underline{\textbf{To find:}}$

$\textsf{Length of AC}$

$\underline{\textbf{Solution:}}$

$\mathsf{In\;\triangle\;ABC,}$

$\mathsf{Using,}\;\boxed{\mathsf{cos\theta=\dfrac{Adjacent\;side}{Hypotenuse}}}$

$\implies\mathsf{cos\,30^\circ=\dfrac{AC}{AB}}$

$\implies\mathsf{\dfrac{\sqrt{3}}{2}=\dfrac{AC}{6}}$

$\implies\mathsf{AC=\dfrac{\sqrt{3}}{2}{\times}6}$

$\implies\boxed{\mathsf{AC=3\sqrt{3}}}$

$\underline{\textbf{Answer:}}$

$\mathsf{Option\;(A)\;is\;correct}$

$\underline{\textbf{Find more:}}$

In rectangle ABCD I(AB) =8CM,I9(BD)=10CM.find l(AD)

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