Question : If $\theta$ is an acute angle and $\cos\theta=\frac{11}{17}$, what is the value of $\tan\theta$?
Option 1: $\frac{4 \sqrt{10}}{11}$
Option 2: $\frac{13}{11}$
Option 3: $\frac{2 \sqrt{42}}{11}$
Option 4: $\frac{2 \sqrt{42}}{17}$
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Correct Answer: $\frac{2 \sqrt{42}}{11}$
Solution :
Given: $\cos\theta=\frac{11}{17}$
Let the Base = 11 units and the Hypotenuse = 17 units
We know,
$\text{Perpendicular} = \sqrt{(\text{Hypotenuse})^2–(\text{Base})^2}$
So, $\text{Perpendicular} = \sqrt{17^2–11^2}=\sqrt{289–121}=\sqrt{168}=2\sqrt{42}$ units
Therefore, $\tan\theta=\frac{\text{Perpendicular}}{\text{Base}}=\frac{2\sqrt{42}}{11}$
Hence, the correct answer is $\frac{2\sqrt{42}}{11}$.
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