Question
Download Solution PDFIn a triangle PQR, the angle PQR is a right angle. The angle PRQ is 60° and the length of side PR is 20 cm. What is the length of the side QR?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Triangle PQR is Right angled triangle
∠PQR = 90°
∠PRQ = 60°
PR = 20 cm
Concept used:
Sum of all interior angles of a triangle is 180°
sin θ = P/H
Calculation:
Sum of all interior angles = 180°
⇒ ∠PQR + ∠PRQ + ∠RPQ = 180°
⇒ 90° + 60° + ∠RPQ = 180°
⇒ ∠RPQ = 180° – 150° = 30°
Now, sin 30° = P/H
⇒ sin 30° = QR/PR
⇒ 1/2 = QR/20
⇒ QR = 10
∴ The length of side QR is 10 cm
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