A ghost on a 135 feet cliff perpendicular 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? Sketch the triangle that matches this scenario with a ruler and protractor, and use this diagram and scales to solve for these distances between the ghost, wolf and cliff. Explain how you got your answer. Solve using the THINK Framework.
can't sketch here , but can do trigonometry
ghost to werewolf ... 135 ' / cos(90º - 16º)
wolf to cliff ... 135 ' * tan(90º - 16º)
To solve this problem using the THINK Framework, we will follow the five steps: Think, Help, Information, Note, and Knowledge. Let's begin:
1. Think:
We need to find the distances between the ghost, werewolf, and the base of the cliff. To do this, we can use trigonometry and the given angle of depression.
2. Help:
To apply trigonometry, we can use the tangent function. The tangent of an angle is equal to the ratio of the length of the opposite side to the length of the adjacent side. Here, the opposite side is the vertical distance between the ghost and the werewolf, and the adjacent side is the horizontal distance between the ghost and the werewolf.
3. Information:
We are given:
- The angle of depression from the ghost to the werewolf: 16 degrees.
- The height of the cliff: 135 feet.
4. Note:
Let's use the variables:
- G = distance between the ghost and werewolf (opposite side)
- H = height of the cliff (adjacent side)
5. Knowledge:
We can solve this using trigonometry (tangent function):
tan(angle) = opposite/adjacent
Here, the opposite side is G, the adjacent side is H, and the angle of depression is 16 degrees.
tan(16) = G/H
Now, let's solve for G:
G = tan(16) * H
Given that H is the height of the cliff (135 feet), we can plug in this value and solve for G.
G ≈ tan(16) * 135
Using a scientific calculator, we find:
G ≈ 41.18 feet
So, the ghost is approximately 41.18 feet away from the werewolf.
To find the distance between the werewolf and the base of the cliff, we need to subtract the horizontal distance between the ghost and the werewolf from the total horizontal distance between the cliff and the werewolf.
The horizontal distance between the ghost and the werewolf is the adjacent side, which is H.
H ≈ 135 feet
Therefore, the distance between the werewolf and the base of the cliff is:
135 - 41.18 ≈ 93.82 feet.
This is the approximate distance from the werewolf to the base of the cliff.