Question

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

Answer 1

  ∠P = 60° and   ∠R = 30°

Step-by-step explanation:

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

Find:∠P and ∠R.

Solution:

 In ΔPQR, ∠Q = 90°

 So PR is the hypotenuse = 6cm

 If ∠R = θ, then PQ is the opposite and QR is the adjacent.

 QR = √6² - 3² = √36 - 9 = √27 = 3√3

 Sin R = PQ / hypotenuse = 3/6 = 1/2

 Therefore ∠R = 30°

 Sin P = QR / hypotenuse =  3√3/ 6 =  √3 /2

  ∠P = 60°