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JAMB Mathematics 1988 Question 46

Question 46

Loci

PQR is a triangle in which PQ = 10cm and QP̂R = 60°. S is a point equidistant from P and Q. Also, S is a point equidistant from PQ and PR. If U is the foot of the perpendicular from S on PR, find the length SU in cm to one decimal place.

  1. A.2.7
  2. B.2.9
  3. C.3.1
  4. D.3.3
Show the answer and explanation

Answer: B (2.9)

Explanation

S is on the perpendicular bisector of PQ, so it is above the midpoint, 5cm from P. S is also on the bisector of angle P, which makes 30° with PQ. Its distance from PQ (equal to SU) is 5 tan 30° = 2.89 ≈ 2.9cm.