Question

prove that In a triangle other than equilateral triangle , angle opposite to longer side is 2/3of right angle .​

Answer 1

Step-by-step explanation:

Consider △PQR where PR is the longest side

So we get PR>PQ

i.e. ∠Q>∠R..(1)

We also know that PR>QR

i.e. ∠Q>∠P..(2)

By adding both the equations

∠Q+∠Q>∠R+∠P

So we get

2∠Q>∠R+∠P

By adding ∠Q on both LHS and RHS

2∠Q+∠Q>∠R+∠P+∠Q

We know that ∠R+∠P+∠Q=180

So we get

3∠Q>180

By division

∠Q>60

So we get

∠Q>3/2

(90 )

i.e. ∠Q> 3/2of a right angle

Therefore, it is proved that in a triangle, other than an equilateral triangle, angle opposite the longest side is greater 2/3of a right angle.

Answer 2

Answer:

Therefore, it is proved that in a triangle, other than an equilateral triangle, angle opposite the longest side is greater 32 of a right angle.