Answer:
- distance: 19 m
- height: 9 m
Step-by-step explanation:
You want to know the distance and height of a pole observed to have an angle of depression of 6° and an angle of elevation of 21° from a point 2 m high.
Tangent
In a right triangle, the tangent function relates angles to the legs of the triangle:
Tan = Opposite/Adjacent
We can use this relation twice to solve this problem.
Distance
The distance to the pole can be found from ...
[tex]\tan(6^\circ)=\dfrac{\text{man's height}}{\text{distance to pole}}\\\\\\\text{distance to pole}=\dfrac{\text{$2$ m}}{\tan(6^\circ)}\approx19.03\text{ m}[/tex]
The distance of the man from the pole is about 19 meters.
Height
The height of the pole above the man's height is ...
[tex]\tan(21^\circ)=\dfrac{\text{additional height}}{\text{distance to pole}}\\\\\\\text{additional height}=\text{(distance to pole)}\times\tan(21^\circ)\\\\\text{additional height}=(19.03\text{ m})\tan(21^\circ)\approx7.30\text{ m}[/tex]
Since the man's observation point is 2 m above the ground, the height of the pole is ...
pole height = 2 m + 7.30 m = 9.30 m
The height of the pole is about 9 meters.
