Answer:
Step-by-step explanation:
When you draw out that picture (and very good description, btw!) basically what you have is a right triangle that has a base of 32 and a hypotenuse of 45. The right angle is one of the base angles and x is the vertex angle. We need to find the vertex angle before we can find the angle of depression from the second bird to the watcher. The side of length 32 is opposite the angle x, and 45 is the hypotenuse, so the trig ratio we need is the only one that directly relates side opposite to hypotenuse, which is the sin ratio:
[tex]sin(x)=\frac{32}{45}[/tex] and
sin(x) = .711111111
Go to your calculator and hit the 2nd button then the sin button and on your screen you will see:
[tex]sin^{-1}([/tex]
and after that open parenthesis enter in your decimal .711111111 and hit equals. You should get an angle of 45.325. That's angle x. But that's not the angle of depression. The angle of depression is the one complementary to angle x.
Angle of depression = 90 - angle x and
Angle of depression = 90 - 45.325 so
Angle of depression = 44.67 or 44.7 degrees.
