Please Help Me! I'm not so good with trigonometry! Will mark the Brainliest!!! Amanda and Jeremiah are standing on the same side of a large lake. They are separated by a horizontal distance of 4000 ft. Both Amanda and Jeremiah can see a helicopter that is directly above the horizontal distance between them. Amanda’s angle of elevation to see the helicopter is 60° and Jeremiah’s angle of elevation to see it is 30°. What is the distance between Amanda and the helicopter?
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.
