Area of Triangle

Question

A = 1/2absin(x)

Does the pheta, for sine have to be in radians, or can we leave it as degrees?

Answer 1

take a specific example

a triangle formed on a unit circle by a 90 degree angle has Area = .5absin90 = .5(1)(1)(1) = 1/2

sin90 degrees = sinpi/2 radians, so it works either way

just don't confuse them and try to find sin(90 radians) or sin(pi/2 degrees)

confusions come up a couple ways, calculators are set on radian or degree mode.

or you may be confusing this triangle area with the formula for a circle sector which is "radians times radius"

Answer 2

If you are using a calculator to determine sin(x), make sure you have the angle's measurement in the correct mode (radians for radian input, or degrees if the input is in degrees).

Answer 3

The formula is valid regardless of whether theta is expressed in degrees or radians.