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)
Distance of the man from the building = BC
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
∴ TE = tan(71°) × 4.1 = 11.91 m
Hence the height of the building = 11.91 + 2 = 13.91 m.