Answer:
The building is 13.91 m tall
Step-by-step explanation:
The parameters given are;
Angle of elevation to the top of the building = 71°
Angle of depression to the bottom of the building = 26°
Height of the man = 2 m
Therefore, the sight of the man, the man's height, and the distance of the man from the building forms a triangle where:
The hypotenuse side = The sight of the man to the bottom of the building
Hence;
In ΔABC, A being at the eye level or head level of the man, B at the foot and C at the bottom of the building
∴ ∠A + Angle of depression to the bottom of the building = 90°
∠A = 90° - 26° = 64°
∠B = 90° and ∠C = 26° (Sum of angles in a triangle)
![Tan(C) = \frac{AB}{BC}](https://tex.z-dn.net/?f=Tan%28C%29%20%3D%20%5Cfrac%7BAB%7D%7BBC%7D)
Distance of the man from the building = BC
![Tan(26) = \frac{2}{BC}](https://tex.z-dn.net/?f=Tan%2826%29%20%3D%20%5Cfrac%7B2%7D%7BBC%7D)
![BC= \frac{2}{ Tan(26) } = 4.1 \, m](https://tex.z-dn.net/?f=BC%3D%20%5Cfrac%7B2%7D%7B%20Tan%2826%29%20%7D%20%3D%204.1%20%5C%2C%20m)
Given that the angle of elevation to the top of the building = 71°, we have;
ΔAET
Where:
A is at the head level of the man,
E is the point on the building directing facing the man and
T is the top of the building
Hence AE = BC and ∡TAE = 71°
TE + AB= The height of the building
![Tan(TAE) = \dfrac{TE}{AE}\\\\Tan(71) = \dfrac{TE}{4.1}](https://tex.z-dn.net/?f=Tan%28TAE%29%20%3D%20%5Cdfrac%7BTE%7D%7BAE%7D%5C%5C%5C%5CTan%2871%29%20%3D%20%5Cdfrac%7BTE%7D%7B4.1%7D)
∴ TE = tan(71°) × 4.1 = 11.91 m
Hence the height of the building = 11.91 + 2 = 13.91 m.