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Question

   the point (-5,8) is located on the terminal arm of <A in standard position

A) Sketch 
B) determine the measure of <A and <B.

Answer 1

A) The point (-5, 8) is located on the terminal arm of <A in standard position.

The above coordinate pair in second quadrant.

Angle A is in second quadrant.

From Pythagorean theorem,

r² = x² + y²

r = √[5² + 8²]

r = √(25 + 64)

r = √89

 

B)

Find the angle of A:

sinA = opposite side/hypotenuse

sinA = 5/√89

= 5/9.43

A = sin ^-1 (0.5302)

A = 32.0205°

Sum of the angles in a triangle 180°

We now that <C = 90° and <A = 32.0205°

B = 180° - ( 90° + 32.0205°)

B = 57.9794°

<A = 32.0205° <B = 57.9794°.