3.) 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 Matt?
We can use trigonometry to solve this problem. Let's draw a diagram first:
```
|\
| \
305| \ x
| \
|____\
d
```
We know that the angle of depression from Matt to the boat is 42 degrees. This means that the line of sight from Matt to the boat makes an angle of 42 degrees with the horizontal. We want to find the distance between Matt and the boat, which we'll call "d". We can use the tangent function to find d:
```
tan(42) = opposite / adjacent
tan(42) = 305 / x (opposite is 305 because that's the height of the cliff)
x = 305 / tan(42)
x ≈ 323.4 feet
```
So the boat is approximately 323.4 feet away from Matt.
Answers & Comments
We can use trigonometry to solve this problem. Let's draw a diagram first:
```
|\
| \
305| \ x
| \
|____\
d
```
We know that the angle of depression from Matt to the boat is 42 degrees. This means that the line of sight from Matt to the boat makes an angle of 42 degrees with the horizontal. We want to find the distance between Matt and the boat, which we'll call "d". We can use the tangent function to find d:
```
tan(42) = opposite / adjacent
tan(42) = 305 / x (opposite is 305 because that's the height of the cliff)
x = 305 / tan(42)
x ≈ 323.4 feet
```
So the boat is approximately 323.4 feet away from Matt.