Question

triangle PQR is right angled isosceles triangle, right angled at R. Find the value of sin P.
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Answer 1

Answer:

in an isosceles triangle, the angles opposite to the equal sides are equal. Now, the triangle PQR is right angled at R. Therefore, the sum of the other two angles = 180 - 90 = 90 degrees. Since, the angles P and Q are equal, as the triangle is isosceles, each of these angles is 45 degrees. Hence, sinP = sin45 =1/√2=√2/2, upon rationlising the denominator.

Answer 2

Step-by-step explanation

angle pqr is right angled at r

so , angle p and angle q will be equal since it is an isoceles triangle and sum of the angles = 180 degree

so they both are = angle p+ angle q

angle p + angle q + angle r= 180 degree

angle p+angle q + 90 degree= 180 degree

angle p+ angle q = 90 degree

as angle p= angle q (isoceles triangle)

2 x angle p= 90 degree

so angle p= angle q= 45 degree

now ,

this sum can be solved in 2 ways

but the part written above is to be shown

1. by Pythagoras theorem,

pr2+qr2=pq2

we know that pr=qr since triangle is an isoceles triangle.

let pr be x

x2+x2=pq2

2x2=PQ2

HENCE ,

PQ=

$\sqrt{2} x$

now , sin theta = perpendicular/hypotenuse

sin of angle p=qr/pq

$\sin(p) = x \div \sqrt{2} x \\ = 1 \div \sqrt{2}$

this was one method

second one is easier

2. we know that angle p=45 degree

so , sin p=sin45

now , refer to t-ratio table for standard angles

sin 45 = 1/√2

hence

$\\ \sin(p) = \\ 1 \div \sqrt{2}$

this is the easier method if it is allowed .

please mark this answer as brainliest