Question

The picture give below a square PQRS is drawn in the triangle ABC.the triangle QRB are isosceles triangle.calculate the probability of dot put without looking within in the square​

Answer 1

⟹∠TQR=15⁰

Step-by-step explanation:

(i)Because PQRS is a square

∠PSR=∠QRS=90⁰

Now In △SRT

∠TSR=∠TRS=60⁰

∠PSR+∠TSR=∠QRS+∠TRS

⟹∠TSP=∠TRQ

Now in △TSP and △TRQ

TS=TR

∠TSP=∠TRQ

PS=QR

Therefore , △TSP≡△TRQ

So PT=QT

(ii) Now in △TQR,

TR=QR(RQ=SR=TR)

∠TQR=∠QTR

And ∠TQR+∠QTR+∠TRQ=180

⟹∠TQR+∠QTR+∠TRS+∠SRQ=180

⟹2(∠TQR)+60+90=180 (∠TQR=∠QTR)

2(∠TQR)=30

⟹∠TQR=15⁰

Answer 2

Because PQRS  is a square

∠PSR=∠QRS=90∘

Now In △SRT

  ∠TSR=∠TRS=60∘

∠PSR+∠TSR=∠QRS+∠TRS

⟹∠TSP=∠TRQ

Now in △TSP and △TRQ

                       TS=TR

                   ∠TSP=∠TRQ

               PS=QR

Therefore , △TSP≡△TRQ

     So  PT=QT

 

(ii)                Now in △TQR,

TR=QR(RQ=SR=TR)

∠TQR=∠QTR

And ∠TQR+∠QTR+∠TRQ=180

⟹∠TQR+∠QTR+∠TRS+∠SRQ=180

⟹2(∠TQR)+60+90=180  (∠TQR=∠QTR)

2(∠TQR)=30

⟹∠TQR=15∘

hope it helps you

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