Read the given information carefully and answer the questions given beside: (A…
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Read the given information carefully and answer the questions given beside: (A set of 2 questions) Five friends Teenu, Bani, Chandni, Dev and Joy are playing Hide and Seek and standing randomly. Bani is to the northeast of Joy. Dev is 20 m to the east of Joy, who is 60 m to the west of Teenu. Chandni is to the northwest of Dev and in the line of Joy and Bani. Dev is 40 m to the south of Bani.
What angle does Bani make at the point where Teenu is standing while Joy, Dev and Teenu are in the same line?
- A.
135°
- B.
45°
- C.
90°
- D.
60°
Attempted by 5 students.
Show answer & explanation
Correct answer: B
Place Joy at (0,0). Then Dev is 20 m east of Joy so Dev = (20,0), and Teenu is 60 m east of Joy so Teenu = (60,0). Bani is 40 m north of Dev, so Bani = (20,40).
Compute distances: Dev–Bani = 40 m and Dev–Teenu = 40 m.
Vectors from Dev: Dev→Bani = (0,40) (straight north) and Dev→Teenu = (40,0) (straight east). These vectors are perpendicular, so the angle at Dev is 90°.
Triangle Bani–Dev–Teenu is a right isosceles triangle (legs 40 m), so the two non-right angles are equal and each is 45°.
Answer: 45°