Abird catches a fish and flies 100 yards in a straight line at an angle of elevation x degrees from the ground. after flying for 100 yards the bird drops the fish. the fish lands at a spot y yards horizontally from where the bird caught it. what is x?
a.)cos -1 y/100

b.)sin -1 y/100

c.)tan -1 y/100

d.)cos -1 100/y

e.)sin -1 100/y

 Hello there! The correct answer is A.

If the bird flies 100 yards with an angle of elevation of x from the ground, then you could think this as a tringle rectangle, where the hypotenuse is 100 yards, the opposite cathetus is sin(x)*100 and this represents the height at which the bird dropped the fish, not really useful here.

The adjacent cathetus us 100*cos(x), in this case, you are calculating the displacement adjacent to them (because the angle is with respect to the ground) and knowing that the fish lands in a translated y yards horizontally we could write: y = cos(x)*100

now we want to isolate x:

y/100 = cos(x)

arcos(y/100) = arcos(cos(x)) = x

x = arcos(y/100) (or cos-1(y/100) like in the option A)

then, knowing the value of y, we could obtain the angle x with that equation.