Question

Triangle PQR is a right angled isosceles triangle right angled at R. Find the value of sinP

Answer 1

Sin P= 1/root2 as the given triangle is 45-45-90 triangle

Answer 2

Answer:

sinP = sin45°

Step-by-step explanation:

In the question,

We have been provided a triangle right-angled at R and the sides are equal.

PQR is an isosceles triangle.

Now,

Let us say the side of the triangle is = x

So,

Length of the height and base both = x

So,

Using the Pythagoras theorem,

PQ² = PR² + QR²

PQ² = x² + x² = 2x²

PQ = x√2

Now,

In the triangle using the trigonometric principle,

$sinP=\frac{QR}{PQ}\\sinP=\frac{x}{x\sqrt{2}}\\sinP=\frac{1}{\sqrt{2}}\\sinP=sin45$

Therefore, the value of angle sinP is given by,

sinP = sin45°

Hence, found.