Question

In ∆PQR, right-angled at Q, PQ = 3 cm and PR = 6 cm. Determine ∠P and ∠R.

Answer 1

SOLUTION :

Given :

In ΔPQR, right angled at Q, PQ = 3 cm and PR = 6 cm

In ∆PQR , By Pythagoras theorem,

PR² = PQ² +QR²  

6² = 3² + QR²

36 = 9 + QR²

QR² = √36- 9

QR = √27 = √3×3×3

QR = 3√3

sin R = P/ H = PQ/PR

=  3/6  

=½

sin R = sin 30°

∠R=30°

In ∆PQR,  

∠P + ∠Q + ∠R = 180°

[Sum of angles in a ∆ = 180°]

∠P + 90° + 30° = 180°  

∠P + 120°  = 180°  

∠P = 180° - 120°

∠P = 60°

Hence, ∠R = 30° and ∠P = 60°

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Answer 2

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