To find the angle of the helicopter, we are going to take advantage of the fact the the sum of the interior angles of a triangle is always 180°. Lets denote that angle with [tex]h[/tex], so:
[tex]h+60+30=180[/tex]
[tex]h+90=180[/tex]
[tex]h=180-90[/tex]
[tex]h=90[/tex]
Look what we have here: a angle of 90°, so our triangle is a right triangle.
Now, let [tex]x[/tex] be the distance between Amanda and the helicopter. Using the law of sines:
[tex] \frac{x}{sine(30)} = \frac{4000}{sine(90)} [/tex]
Remember that sine of 90 ° is equal to 1, so:
[tex] \frac{x}{sine(30)} = \frac{4000}{1} [/tex]
[tex]x=4000sine(30)[/tex]
[tex]x=2000[/tex]
We can conclude that the distance between Amanda and the helicopter is 2000 feet.
