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.
Algebra.Com
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) (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
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