The coordinates PQR are (5,9) (14,-3), and (2,3) find angle PQR?

Question

without a calculator, PQR is a right angle triangle please help?

Answer 1

Triangle PQR coordinates are P(5,9) , Q(14,-3) , R(2,3)

PQ , QR , RP are the sides of triangle PQR.

Distance between points P(5,9) , Q(14,-3) is PQ

PQ² = (14-5)²+(-3-9)² = 9²+(-12) = 81+144 = 225

 

Distance between points Q(14,-3) , R(2,3) is QR

QR² = (2-14)²+(3+3)² = (12)²+(6)² = 144+36 = 180

 

Distance between points R(2,3) , P(5,9) is RP

RP² = (5-2)²+(9-3)² = 3²+6² = 9+36 = 45

 

QR² + RP² = 180 + 45 = 225 = PQ²

Pythagorean theorem for PQR triangle is proved as PQ² = QR² + RP²

So Triangle PQR is Right angled triangle.

Let angle ∠PQR = Θ

sinΘ = RP/PQ = 45/225 = 11.54°

Solution : Angle ∠PQR = 11.54°