Question

How can we say that area of triangle is 1/2 r² sin theta??​

Answer 1

Answer:

Consider an isosceles triangle, ABC whose two sides, AB = AC = 'r' and the included angle (<BAC) is theta. If the triangle has sides as a, b and the included angle is theta, then the general equation for the area of the triangle is (ab/2)*sin theta

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Answer 2

The formula stands for isosceles triangles, theta is the angle between the two equivalent sides.

If you draw the height relative to the base (that is also the bisector) you find the height as R*cos(theta/2) and the half base as R*sin(theta/2)

A=half base * height = R^2 *cos(theta/2)*sin(theta/2)

Using the trigonometric formula: sin(theta)=2*sin(theta/2)*cos(theta/2)

A=1/2*R^2*sin(theta)