A pole stands vertically inside a triangular park ABC . Let the angle of elevation of the top of the pole from each corner of the park be (pi)/(3) . If the radius of the circumcircle of triangle ABC is 2 , then the height of the pole is equal to :

Trigonometric Ratio & Identities: A pole stands vertically inside a triangular park ABC . Let the… | JEE Main 2021

JEE Main 2021 (Online) 18th March Evening ShiftQuestion 1

A pole stands vertically inside a triangular park $ABC$. Let the angle of elevation of the top of the pole from each corner of the park be $\frac{\pi}{3}$. If the radius of the circumcircle of $\triangle ABC$ is $2$, then the height of the pole is equal to :

Trigonometric Ratio & Identities

$\frac{2\sqrt{3}}{3}$$2\sqrt{3}$✓ Correct answer$\frac{1}{\sqrt{3}}$$\sqrt{3}$

Solution

Concept. Equal elevations from $A,B,C$ mean the foot is equally far from all three: it is the circumcentre. Formulas used. (1) $h=d\tan(\text{elevation})$Step 1 - Distance. The foot is at distance $R=2$ from each corner. Step 2 - Height. By (1), $h=2\tan\frac\pi3=2\sqrt3$. Answer: (B)

Trigonometric Ratio & Identities - JEE Mathematics question (JEE Main 2021 (Online) 18th March Evening Shift)

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