SOLUTION: A boy cycles 8km on a bearing of 060°. How far is the boy North of his starting point? Give your answer to 2 s.f.

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Question 1200431: A boy cycles 8km on a bearing of 060°.
How far is the boy North of his starting
point? Give your answer to 2 s.f.

Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

Start facing directly north.
Then turn 60 degrees toward the east (i.e. to the right).
This will align you with the bearing 060°
This is in the northeast quadrant.

Compass Rose:

Image courtesy of Wikipedia.
https://en.wikipedia.org/wiki/File:Compass_rose.png

This is what your rough sketch of the diagram should look like

The boy starts at point P and moves to point Q.
Note that 60+30 = 90.

Let's erase the vertical line and erase the "60 degree" label.
I'll add in a vertical line from Q to drop down to the horizontal line.
It has length x to represent how far north Q is compared to P.

The goal is to have a right triangle, so we can use a trig ratio to determine x.

sin(angle) = opposite/hypotenuse
sin(30) = x/8
x = 8*sin(30)
x = 8*0.5
x = 4
This value is exact.
Make sure your calculator is in degree mode.

Answer: 4 km