b First find the horizontal distance between the falcon and mouse B and the horizontal distance between the falcon and mouse A.
A
a About 647.2 feet
B
b About 239.4 feet
Practice makes perfect
a We are given a diagram that represents a falcon at a height of 200 feet that sees two mice A and B.
We will find the approximate distance z between the falcon and mouse B.
We will write an equation using a trigonometric ratio of the height of the falcon and the distance between the falcon and mouse B. The cosine of 72^(∘) will give us the desired ratio — remember that the cosine of an acute angle θ is the ratio between the lengths of the adjacent side and the hypotenuse.
cos θ = Adjacent/Hypotenuse ⇒ cos 72^(∘) = 200/z
Now we will solve this equation to find z.
The approximate distance z between the falcon and mouse B is 647.2 feet.
b We will find the distance between the two mice y.
To do so, by writing the tangent of the given angles we will first find the horizontal distance between the falcon and mouse B, x+ y, and the horizontal distance between the falcon and mouse A, x. Let's start by finding x+ y by using the tangent of 72^(∘).
The horizontal distance between the falcon and Mouse B is about 615.5 feet. Now we will find the horizontal distance between the falcon and mouse A by using the tangent of 62^(∘).
