Respuesta :
Answer:
[tex]\theta = 12.16^0.[/tex]
Step-by-step explanation:
Given,
Height = 12.6 m
Object distance from the person = 58.5 m
Angle of depression
[tex]tan \theta = \dfrac{P}{B}[/tex]
[tex]tan \theta = \dfrac{12.6}{58.5}[/tex]
[tex]tan \theta = 0.2154[/tex]
[tex]\theta = 12.16^0[/tex]
Hence, angle of depression is equal to [tex]\theta = 12.16^0.[/tex]
The angle of depression of the person's line of sight to the object on the ground is 12.15°.
The information forms a right angle triangle. The person eyes above the ground is the opposite side of the triangle. The object distance from the building in line of the sight is the adjacent side of the right angle triangle.
Therefore,
using trigonometric ratio,
tan Ф = opposite /adjacent
tan Ф = 12.6 / 58.5
tan Ф = 0.21538461538
Ф = tan⁻¹ 0.21538461538
Ф = 12.1549416972
Ф = 12.15°
angle of depression ≈ 12.15°
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