Question

A ghost on a 135 feet cliff perpendicular (at 90 degrees) to the ground looks down at an angle of 16 degrees and sees a

werewolf. How far away is the ghost from the werewolf approximately? How far away is the wolf from the base of the cliff?

Answer 1

To solve this problem you must apply the proccedure shown below:

1. You can make the diagram attached, where the ghost is identified as G and the the werewolf as W. The distance between both of them is y and the distance of the werewolf from the base of the cliff is x.

2. Let's calculate y:

`Cos(16)=(135)/(y)`

`y=(135)/(Cos(16))`

`y=140.44` ft

3. Now, let's calculate x:

`Tan(16)=(x)/(135)`

`x=(135)(Tan(16))`

`x=38.71` ft

The answer are:

• The ghost is 140.44 feet from the werewolf.
• The werewolf is 38.71 feet from the base of the cliff.

Answer 2

Answer: Hello mate!

The cliff has a height of 135 ft and is perpendicular to the ground, then we can think it as a triangle rectangle, where one of the cathetus is equal to 135ft

We know that the ghost looks down at an angle of 16°, then if we consider this angle, the cathetus of 135ft is the adjacent one.

We want to find the distance between the ghost and the werewolf, we need to find the hypotenuse of this triangle rectangle.

we can use the relation of Cos(a) = (Adj cath)/hipotenuse.

then in this case we have: cos(16°) = 135ft/H

then H = 135ft/cos(16°) = 140.4ft

The distance between the ghost and the werewolf is equal to 140.4ft

now we want to know the distance between the wolf and the base of the cliff, this is equivalent to find the other cathetus (the opposite of the angle of 16°) on our triangle.

we can use the tangent relation: tan(a) = (opposite cathetus)/(adjacent cathetus)

tan(16°) = x/135ft

x= 135ft*tan(16°) = 38.7ft

The distance between the werewolf and the base of the cliff is 38.7 feet.