a man two metre tall stands on the same level ground as a vertical pole ,he observe that the angle of elevation of the pole is 21° and the angle of depression of the foot of the pole is 6°.find, correct to the nearest degree a.how far the pole is from the man b.tye height of the pole​



Answer :

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.

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