An Observer on a Ladder 29 feet above level ground looks qt near by building the angle of elevation of the top of the building is 72° and the angle of depression of the base of the building is 39°. find height (H) of the building to the nearest foot.
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```
H (to be found)
|\
| \
| \
| \
| \
| \
| \
|72° \
L | \
o-------- o B (building)
|39°
|
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```
We have a right triangle formed by the observer on the ladder (point L), the base of the building (point B), and a point directly beneath the observer (point O). We can use the tangent function to find the height of the building:
```
tan(72°) = H / LO (1)
tan(39°) = H / OB (2)
```
We want to solve for H, so let's rearrange equation (1) to isolate H:
```
tan(72°) = H / LO
H = LO * tan(72°)
```
Now we can substitute this expression for H into equation (2) and solve for OB:
```
tan(39°) = H / OB
tan(39°) = LO * tan(72°) / OB
OB = LO * tan(72°) / tan(39°)
```
We know that LO is 29 feet, so we can plug in the numbers and solve:
```
OB = 29 * tan(72°) / tan(39°)
OB ≈ 48.7 feet
```
Finally, we can use the Pythagorean theorem to find H:
```
H^2 = OB^2 + BO^2
H^2 = OB^2 + (LO)^2
H^2 = (48.7)^2 + (29)^2
H^2 ≈ 2881.69
H ≈ 53.64 feet
```
Therefore, the height of the building is approximately 53.64 feet.