Locating a car from the 102nd floor observation deck of the empire state building, an observer spots his car at an angle of depression of 5 degrees. if the observation deck is 1250 feet high, how far is his car from the building?
sin5°=1250/hyp
hyp= 1250/sin5°
hyp = ......
14342.14
To find the distance of the car from the building, we need to use trigonometry. We can consider the observation deck as the point where the observer is standing, the base of the building as the starting point, and the car as the end point.
First, let's draw a diagram to visualize the situation. Assume the distance from the building to the car is represented by 'x'. The angle of depression is the angle between the observer's line of sight and the horizontal line.
```
|\
| \
x | \ Observation Deck
| \
| \
|-----\-- Building
1250 ft
```
Now, we can use the properties of a right triangle to solve for 'x'.
In the right triangle formed, the angle of depression is 5 degrees, and the opposite side is the height of the observation deck, which is 1250 feet. The side representing the distance to the car is adjacent to the angle of depression.
We can use the tangent function to relate the angle of depression to the opposite and adjacent sides of the triangle:
tan(angle) = opposite / adjacent
In this case, we have:
tan(5 degrees) = 1250 ft / x
To isolate 'x', we can rearrange the equation:
x = 1250 ft / tan(5 degrees)
Using a scientific calculator, we can find the tangent of 5 degrees and then divide 1250 feet by that value to find the distance 'x'.