Question

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?

Answer 1

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 $h$, so:
$h+60+30=180$
$h+90=180$
$h=180-90$
$h=90$
Look what we have here: a angle of 90°, so our triangle is a right triangle.

Now, let $x$ be the distance between Amanda and the helicopter. Using the law of sines:
$\frac{x}{sine(30)} = \frac{4000}{sine(90)}$
Remember that sine of 90 ° is equal to 1, so:
$\frac{x}{sine(30)} = \frac{4000}{1}$
$x=4000sine(30)$
$x=2000$

We can conclude that the distance between Amanda and the helicopter is 2000 feet.