A point P moves such that it is equidistant from Points Q and R. Find...

A point P moves such that it is equidistant from Points Q and R. Find QR when PR = 8cm and angle PRQ = 30°

Hint: Make a sketch of an isosceles triangle with two of its sides and angles angles.

: PQ (r) = PR (q) = 8cm

: R° = Q° = 30°

Sum of angles in a triangle = 180°

P° + Q° + R° = 180°

P° + 30° + 30° = 180°

P° = 180° - 60°

p° = 120°.

: PQ = r, PR = q, QR = p

Using sine rule:

\(\frac{p}{sinP}\) = \(\frac{q}{sinq}\)

\(\frac{p}{sin120°}\) = \(\frac{8}{sin30°}\)

cross multiply

p = \(\frac{8 X sin120°}{sin30°}\)

p = \(\frac{8 X √3/2 }{1/2}\)

p = 8√3

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