Question

In triange pqr right angled at Q,PQ=3 cm PR=6 find sin r

Answer 1

Answer:

The measurement of angle PRQ = 30°

And, The measurement of angle QPR = 60°

Step-by-step explanation:

Here, PQR is a right triangle,

In which m∠Q = 90°, PQ = 3 cm and PR = 6 cm,

By the law of sine,

\frac{sinR}{PQ}=\frac{sinQ}{PR}

PQ

sinR

=

PR

sinQ

\implies \frac{sinR}{3}=\frac{sin90^{\circ}}{6}⟹

3

sinR

=

6

sin90

∘

\implies sin R = 3\times \frac{sin90^{\circ}}{6}⟹sinR=3×

6

sin90

∘

sin R = \frac{3}{6}=\frac{1}{2}sinR=

6

3

=

2

1

\implies \angle R = 30^{\circ}⟹∠R=30

∘

⇒ \implies \angle PRQ = 30^{\circ}⟹∠PRQ=30

∘

By the property of a triangle,

\angle P+\angle Q+\angle R = 180^{\circ}∠P+∠Q+∠R=180

∘

\implies \angle P + 90^{\circ}+30^{\circ}=180^{\circ}⟹∠P+90

∘

+30

∘

=180

∘

\implies \angle P = 180^{\circ}-120^{\circ}=60^{\circ}⟹∠P=180

∘

−120

∘

=60

∘

\implies \angle QPR = 60^{\circ}⟹∠QPR=60

∘