Question

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

Answer 1

Answer:

sin p=1/√2

Step-by-step explanation:

pqr is a right angled isosceles triangle therefore each angle QPR and pqr are of 45° sin 45°=1/√2

Answer 2

Answer: 1/√2

Step-by-step explanation:

∆ PQR is given as a right-angled isosceles triangle where angle R = 90° as shown in the figure attached below.

Since the triangle PQR is isosceles, therefore,

PR = QR …… [∵ sides of an isosceles triangle are of equal length]

∴ ∠RQP = ∠QPR …. [∵ angles opposite to equal sides are equal] …. (i)

In ∆ PQR, using the angle sum property, we get

∠R + ∠RQP + ∠QPR = 180°

⇒90° + ∠RQP + ∠QPR = 180°

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

⇒ 2 * (∠RQP) = 180° - 90° = 90°

⇒ angle RQP = 90° / 2 = 45°

∴ angle RQP = angle QPR = 45°

Thus,  

The value for sin P where angle P = 45° is,

= sin 45°

= 1/√2