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Sagot :
Given the 22 m. horizontal distance and the angles of elevation of 26°
and 31° gives the height of the building as approximately 2.49 meters.
How can the height of the building be found?
Horizontal distance from the building = 22 m
Angle of elevation to the top of the roof = 26°
Angle of elevation to the top of the antenna = 31°
Height of his eyes from the ground = 1.53 m
Required:
The height of the antenna.
Solution:
In a right triangle, we have relative to an angle of the triangle, we have;
Opposite side = Adjacent side
Height of the building + Height of antenna = [tex]1.53 + 22 \times tan \left(31^{\circ} \right)[/tex] ≈ 14.75
Which gives;
Height of the building = [tex]1.53 + 22 \times tan \left(26^{\circ} \right)[/tex] ≈ 12.26
- Height of antenna = Height of the building + Height of antenna - Height of the building
Therefore;
Height of the antenna ≈ 14.75 - 12.26 ≈ 2.49
- Height of the antenna ≈ 2.49 m
Learn more about trigonometric tangent ratio here:
https://brainly.com/question/24415242
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