A point P moves such that it is equidistant from Points Q...
A point P moves such that it is equidistant from Points Q and R. Find QR when PR = 8cm and angle PRQ = 30°
4√3cm
8cm
8√3cm
4cm
Correct answer is C
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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