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Mathematics · Introduction to Trigonometry · NCERT Examples

Example 7

A complete, independently verified solution for NCERT Example 7.

Mathematics · Chapter 8 · NCERT Examples

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Verified NCERT questions and solutionsSolutions are checked independently and follow the supplied NCERT chapter edition.

NCERT Example

Example 7

special angles · complementary angles

In right triangle PQR, right-angled at Q, PQ = 3 cm and PR = 6 cm. Find angles QPR and PRQ.

Right triangle PQR, right-angled at Q, with PQ 3 centimetres and PR 6 centimetres.
Figure 8-20 from the supplied NCERT chapter.

Solution

Board-exam working:

sin⁡R=PQPR=36=12\sin R=\frac{PQ}{PR}=\frac36=\frac12
∠PRQ=30∘\angle PRQ=30^\circ

The two acute angles of a right triangle are complementary.

∠QPR=90∘−30∘=60∘\angle QPR=90^\circ-30^\circ=60^\circ

Final answer

∠QPR = 60° and ∠PRQ = 30°.