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In triangle PQR, if angle P = 30 degrees and angle Q = 60 degrees, what is the l

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Question: In triangle PQR, if angle P = 30 degrees and angle Q = 60 degrees, what is the length of side PR if PQ = 10 cm?

Options:

  1. 5 cm
  2. 8.66 cm
  3. 10 cm
  4. 12 cm

Correct Answer: 8.66 cm

Solution: 

Using the sine rule: PR/sin(30) = PQ/sin(60) => PR = 10 * sin(30)/sin(60) = 10 * 0.5/√3/2 = 10 * 0.5 * 2/√3 = 10/√3 ≈ 8.66 cm.

In triangle PQR, if angle P = 30 degrees and angle Q = 60 degrees, what is the l

Practice Questions

Q1
In triangle PQR, if angle P = 30 degrees and angle Q = 60 degrees, what is the length of side PR if PQ = 10 cm?
  1. 5 cm
  2. 8.66 cm
  3. 10 cm
  4. 12 cm

Questions & Step-by-Step Solutions

In triangle PQR, if angle P = 30 degrees and angle Q = 60 degrees, what is the length of side PR if PQ = 10 cm?
  • Sine Rule – The sine rule relates the lengths of sides of a triangle to the sines of its angles, allowing for the calculation of unknown side lengths when certain angles and sides are known.
  • Triangle Angle Sum – The sum of the angles in a triangle is always 180 degrees, which can help in determining unknown angles.
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