Question

In ∆PQR ∠Q=90°, ∠R=30°,PR=10cm the find the side PQ and QR​

Answer 1

Answer:

Hypotenuse = 10 cm

QR is Base  = 10 . cos 30 = 10 x root3/2= 5 root 3 = 8.66 cm

PQ is perp   = 10 sin 30 = 10 x 1/2 = 5 cm

Step-by-step explanation:

Answer 2

Given: In ∆PQR ∠Q=90°, ∠R=30°, and PR=10cm.

To find: The sides PQ and QR​

Solution: From the given information and the figure, we understand that traingle PQR is a right angled triangle.

Hence we can make use of the trigonometric functions.

We know, sinθ = perpendicular/hypotenuse and cosθ = base/hypotenuse.

According to the figure,

sin 30° = PQ/10 cm

⇒ 1/2 = PQ/10 cm

⇒ PQ = 10/2 cm

⇒ PQ = 5 cm

cos 30° = QR/10 cm

⇒ √3/2 = QR/10 cm

⇒ QR = √3/2 × 10 cm

⇒ QR = 0.866 × 10 cm

⇒ QR = 8.66 cm

Answer: PQ = 5 cm and QR = 8.66 cm