Question

A bird caught a fish on the waters surface and flew in a straight line diagonal to the water for 100 yards. Then, it dropped the fish straight down. The fish landed at a spot 50 yards away horizontally from the point where the bird caught it.

Select the correct answers.


The bird flies at an angle of 1. ______ degrees from the water, and its height from the ground when it drops the fish is 2. _____ yards.


Blank 1 choices:
A) 30
B) 60
C) 78.7

Blank 2 choices:
A) 8.6
B) 86.6
C) 111.8


Random answers will be reported!

Answer 1

The answers should be B)60 and B) 86.6

Answer 2

1. B

2. B

Explanation:

** Attached picture of the situation

The bird caught the fish at point A, flew until B (which is 100 yds away, dropped the fish at C (which is horizontally 50 yards from A).

1.

We want the angle that the bird creates with the water (horizontal). It is angle BAC. With respect to the right triangle, we can say that we know "hypotenuse" and "adjacent" side to angle BAC. cosine relates hypotenuse and adjacent, thus we can write:

`Cos(BAC)=(50)/(100)\\Cos(BAC)=(1)/(2)\\BAC=Cos^(-1)((1)/(2))\\BAC=60`

correct answer is B

2.

Here, we want to find the distance (length) of segment BC. With respect to the angle BAC (we found to be 60), we can say BC is "opposite". We know hypotenuse to be 100. So let's use sine, since sine is ratio of opposite to hypotenuse. Thus, we can write:

`Sin(BAC)=(BC)/(100)\\Sin(60)=(BC)/(100)\\BC=Sin(60)*100\\BC=86.6`

correct answer is B