Given that TanA= -0.5774, find A if 360°<A<540°

Answer 1

We know that TanA = opposite/adjacent, so we can set up a right triangle where A is an angle in the second quadrant (since Tan is negative) and label the opposite side as x and the adjacent side as 1.

Using the Pythagorean theorem, we can solve for the hypotenuse:

h = sqrt(x^2 + 1^2)

Now we can use the given information that 360° < A < 540° to determine the reference angle for A:

reference angle = A - 360°

reference angle = 540° - A

Since the tangent function is negative in the second and fourth quadrants, we know that the reference angle is either 119.036° or 299.036°.

Now we can set up the equation:

TanA = -0.5774

Tan(reference angle) = -0.5774

And solve for the angle:

reference angle = arctan(-0.5774)

reference angle = -29.744°

Since we know that A is in the second quadrant, we add 180° to the reference angle to get:

A = 150.256°

Therefore, A = 150.256° satisfies the conditions of 360° < A < 540° and TanA = -0.5774.