A chimney of 20 m height standing on the top of a building subtends an angle whose tangent is 1 6 at a distance of 70 m from the foot of the building, then the height of building is

Step-by-step solution

Given, tan ⁡ α = 1 6 tan ⁡ α + β = tan ⁡ α + tan ⁡ β 1 - tan ⁡ α tan ⁡ β h + 20 70 = 1 6 + h 70 1 - 1 6 ⋅ h 70 h + 20 70 = 70 + 6 h 420 - h ⇒ h = 50 Hence, 50 m is correct choice.