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In triangle PQR, if angle P = 30 degrees and angle Q = 45 degrees, what is the l

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Question: In triangle PQR, if angle P = 30 degrees and angle Q = 45 degrees, what is the length of side PR if PQ = 10 cm?

Options:

  1. 5 cm
  2. 7.5 cm
  3. 8.66 cm
  4. 10 cm

Correct Answer: 8.66 cm

Solution: 

Using the sine rule, PR = PQ * (sin(Q) / sin(P)) = 10 * (sin(45) / sin(30)) = 10 * (√2/2 / 1/2) = 10 * √2 = 8.66 cm.

In triangle PQR, if angle P = 30 degrees and angle Q = 45 degrees, what is the l

Practice Questions

Q1
In triangle PQR, if angle P = 30 degrees and angle Q = 45 degrees, what is the length of side PR if PQ = 10 cm?
  1. 5 cm
  2. 7.5 cm
  3. 8.66 cm
  4. 10 cm

Questions & Step-by-Step Solutions

In triangle PQR, if angle P = 30 degrees and angle Q = 45 degrees, what is the length of side PR if PQ = 10 cm?
  • Triangle Angle Sum – Understanding that the sum of angles in a triangle is 180 degrees.
  • Sine Rule – Applying the sine rule to find unknown sides in a triangle based on known angles and sides.
  • Trigonometric Ratios – Using sine values for specific angles (30 degrees and 45 degrees) to calculate side lengths.
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