Question

2. In the figure▲PQR is a right triangle , <P = 300

and PR = 12 cm ,

(a) Find the length of PQ

(b) Find the length of QR
​

Answer 1

Answer:

(a) PQ=6√3 cm

(b) QR= 6cm

Step-by-step explanation:

Since it is a right angled triangle and ∠P=30°.

∠R = 60° ....( Angle sum property )

So,

It is a 30°-60°-90° triangle now.

We know that,

If the given triangle is of type 30°-60°-90° then

• Side opposite to 30° angle is half of the hypotenuse
• And side opposite to 60° angle is √3/2 times the hypotenuse.

Here,

Thus,

Hypotenuse PR = 12 cm ...(Given)

The side opposite to 30° is QR.

Therefore, QR= 1/2 × 12 = 6cm

And

The side opposite to 60° is PQ.

Therefore, PQ= √3/2 × 12 = 6√3cm.