JEE 2022 — Mathematics PYQ

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Question

JEE 2022 — Mathematics PYQ

JEE | Mathematics | 2022

The angle of elevation of the top P of a tower from the feet of one person standing due South of the tower is 45° and from the feet of another person standing due west of the tower is 30°. If the height of the tower is 5 meters, then the distance (in meters) between the two persons is equal to:

Choose the correct answer:

Explanation

1. South Wale Vyakti ki Doori ( $OA$ )

South direction mein elevation $45^\circ$ hai:

\tan(45^\circ) = \frac{\text{Height}}{\text{Base}} = \frac{h}{OA}

1 = \frac{5}{OA} \implies OA = 5 \text{ meters}

2. West Wale Vyakti ki Doori ( $OB$ )

West direction mein elevation $30^\circ$ hai:

\tan(30^\circ) = \frac{h}{OB}

\frac{1}{\sqrt{3}} = \frac{5}{OB} \implies OB = 5\sqrt{3} \text{ meters}

3. Dono Vyaktiyon ke Beech ki Doori ( $AB$ )

Chunki South aur West ke beech $90^\circ$ ka angle hota hai, hum Pythagoras theorem use karenge:

AB = \sqrt{OA^2 + OB^2}

AB = \sqrt{5^2 + (5\sqrt{3})^2}

AB = \sqrt{25 + (25 \times 3)}

AB = \sqrt{25 + 75} = \sqrt{100}

AB = 10 \text{ meters}

Final Answer:

Dono vyaktiyon ke beech ki doori $10$ meters hai.