In the given diagram, AB is a vertical tower 100 m away from the foot of a 30 storied building CD. The angles of depression from the point C and E, (E being the mid-point of CD), are 35° and 14° respectively. (Use mathematical table for the required values rounded off correct to two places of decimals only.) Find the height of the:
tower AB
Topic: Heights and distances
Answer
Let building height CD = H m and tower height AB = h m.
Given: BD = 100 m, E is midpoint of CD, tan35° ≈ 0.70, tan14° ≈ 0.25.
From the top C: tan35° = (H−h)/100 0.70 = (H−h)/100 H−h = 70 …(1)
From midpoint E: tan14° = (H/2−h)/100 0.25 = (H/2−h)/100 H/2−h = 25 …(2)
(1) − (2): H/2 = 45 H = 90 m.
From (1): 90−h = 70 h = 20 m.
Answer: Tower AB = 20 m.
The angles of depression equal the corresponding angles of elevation because the horizontal lines are parallel. For each right triangle, tanθ = vertical difference / horizontal distance.