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A bird 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

Verified Answer :

The angle of elevation can be solved using B.)sin -1 y/100, which makes use of trigonometric functions.

facundo3141592

Answer:  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 100cos(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.

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