Question

pqr is right angle isosceles triangle right angled at r find value of sin p​

Answer 1

Answer: [1 / √2]

Explanation:

In right angled isosceles ∆ PQR, we are given

∠R = 90°

Also, since ∆ PQR is an isosceles triangle

∴ PR = QR …. [∵ atleast two sides of an isosceles triangle are equal in length]

∴ ∠P = ∠Q ….. [∵ angles opposite to equal sides are also equal] …. (i)

Now, applying angle sum property to right-angled isosceles ∆ PQR, we get

∠P + ∠Q + ∠R = 180°

⇒ 2*∠P = 180° - 90° = 90° ….. [from (i)]

⇒ ∠P = 90°/2 = 45°

∴ ∠P = ∠Q = 45° ….. (ii)

Thus, the value of sin P is given as,

= sin 45° ….. [from (ii) ∠P = 45°]

= 1 / √2

Answer 2

Explanation :

∆PQR is a right isosceles ∆

•°• PR = QR

We know that, angles opposite to equal sides are also equal.

•°• Angle P = angle Q

In ∆PQR, applying angle sum property,

Angle P + angle Q + angle R = 180°

=> Angle P + Angle P + 90° = 180°

=> 2AngleP = 90°

=> Angle P = 45°

Now,

SinP = Sin45°

=> SinP = 1/√2

Hence, value of SinP = 1/√2