Question

The angle of elevation of the top of a tower is found to be 30° ± 0.5° from a point 300 ± 0.1m from the base. Estimate the height of the tower​

Answer 1

Answer:

100√3  ±  2.67

Step-by-step explanation:

Tan θ = Perpendicular / Base

Perpendicular = Height of tower

Base = 300 ± 0.1 mm

θ = Angle of Elevation = 30° ± 0.5°

=> Perpendicular = Base * Tanθ

=> Height of tower =  (300 ± 0.1) * Tan (30° ± 0.5°)

=> Height of tower =  (300 ± 0.1) * (Tan (30°)  ± Tan0.5))/(1 ± Tan30° *Tan0.5)

=> Height of tower =  (300 ± 0.1) * (Tan (30°)  ± 0.0087))/(1)

=> Height of tower = 300 * Tan 30°  ±  300*0.0087  ±  Tan (30°)0.1

=> Height of tower = 100√3  ±  2.61   ±   0.06

=> Height of tower = 100√3  ±  2.67