Question

In △PQR, if hypotenuse PR = 12, PQ = 6 then what is the measure of ∠P?

Answer 1

ans:60°

Step-by-step explanation:

PR=12

PQ=6

as it has an hypotenuse PR so it is a right angle triangle .

it means <Q =90°

cosQ=PQ/PR

cosQ = 6/12

cosQ =1/2

Q=π/3

therefore Q=60°

Answer 2

Answer:

Given: In ∆PQR , if hypotenuse PR =12, PQ = 6

To find: Angle P

Solution:

In ∆PQR , if hypotenuse PR =12, PQ = 6 .....( Given)

Also, In ∆PQR, Angle P = 90° ........( From figure)

So,

PQ² + QR² = PR²............( Pythagoras theorem)

6² + QR² = 12²

QR² = 12² - 6²

= 144 -36

QR² = 108

QR = 6✓3 ......... ( Taking out positive square roots

from both sides)

But,

QR = ✓3/2 ( hypotenuse)

QR = ✓3/2 ( 12 )

QR= 6✓3

Therefore,

Angle P = 60° .......( Converse of 30° 60° 90° ∆ theorem)