Answer to Question #140355 in Trigonometry for Rio

Question

From a position on the beach, Amelia can see two buoys that mark the turning points for a canoe race. The first buoy is in the lake 500 m straight ahead of Amelia. The angle from the first buoy, to Amelia, to the second buoy is 67°. If the buoys are 700 m apart, what is the angle from the first buoy to the second buoy to Amelia?

Answer 1

Y=height of Amelia

X⁰angle to second bouy

Y/500=tan67⁰

Y=500xtan67⁰

Y=826m

Tanx=826/1200

Tanx=0.6883

X⁰=34.54⁰