Learning Resources

Investigation 9: Related Angles

Test yourself

First construct a diagram containing the given information:
        

The related angle is 180° - 118° or 62°.

First find the coordinates of P:  4 cos 62° = 1.88 and 4 sin 62° = 3.53

Since the angle is in the second quadrant the x-coordinate is negative and the y-coordinate is positive. Thus x-coordinate = -1.88  and y-coordinate = 3.53 which gives:  P( -1.88 , 3.53)

Next find the coordinates of R:   8 cos 62° = 3.76 and  8 sin 62° = 7.06

Again the angle is in the second quadrant so the x-coordinate is negative and the y-coordinate is positive. Thus x-coordinate = -3.76  and y-coordinate = 7.06 which gives:  P( -3.76 , 7.06)

Challenge: The coordinates of R are double that of P. Use similar triangles to prove why this must be so.