2.) Matt is standing on top of a cliff 305 feet above a lake. The measurement of the angle of depression to a boat on the lake is 42°. How far is the boat from the base of the cliff?
We can solve this problem using trigonometry. Let's call the distance from the boat to the base of the cliff "x". Then we can set up the following equation:
tan(42°) = 305 / x
We can solve for x by multiplying both sides by x and then dividing by tan(42°):
x = 305 / tan(42°)
Using a calculator, we find that:
x ≈ 292.8 feet
Therefore, the boat is about 292.8 feet from the base of the cliff.
We can use trigonometry to solve this problem. Let's draw a diagram:
```
|\
| \
| \ (boat)
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
|______________\
(cliff) x
```
We are given that the angle of depression is 42° and the height of the cliff is 305 feet. Let's call the distance from the base of the cliff to the boat "x". Then we have:
```
tan(42°) = 305 / x
```
We can solve for "x" by multiplying both sides by "x" and dividing both sides by tan(42°):
```
x = 305 / tan(42°)
```
Using a calculator, we get:
```
x = 305 / 0.9004 ≈ 339.1
```
Therefore, the boat is approximately 339.1 feet from the base of the cliff.
Answers & Comments
Answer:
We can solve this problem using trigonometry. Let's call the distance from the boat to the base of the cliff "x". Then we can set up the following equation:
tan(42°) = 305 / x
We can solve for x by multiplying both sides by x and then dividing by tan(42°):
x = 305 / tan(42°)
Using a calculator, we find that:
x ≈ 292.8 feet
Therefore, the boat is about 292.8 feet from the base of the cliff.
We can use trigonometry to solve this problem. Let's draw a diagram:
```
|\
| \
| \ (boat)
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
|______________\
(cliff) x
```
We are given that the angle of depression is 42° and the height of the cliff is 305 feet. Let's call the distance from the base of the cliff to the boat "x". Then we have:
```
tan(42°) = 305 / x
```
We can solve for "x" by multiplying both sides by "x" and dividing both sides by tan(42°):
```
x = 305 / tan(42°)
```
Using a calculator, we get:
```
x = 305 / 0.9004 ≈ 339.1
```
Therefore, the boat is approximately 339.1 feet from the base of the cliff.