-
Two posts are x metres apart and the height of one is double that of the other. If from the mid-point of the line joining their feet, an observer finds the angular elevations of their tops to be complementary, then the height (in metres) of the shorter post is
-
-
x 2 √2 -
x 4 - x √2
-
x √2
-
Correct Option: A
CD = h metre, AB = 2h metre
| OB = OD = | metre | 2 |
From ∆OCD,
| tan θ = | = | ..........(i) | ||
| x | ||||
| 2 |
From ∆OAB,
| tan (90° – θ) = | BO |
| ⇒ cotθ = | = | ..........(ii) | ||
| x | ||||
| 2 |
Multiplying both equations,
| tanθ .cotθ = | × | |||
| x | x |
⇒ x2 = 8h2
[∵ tanθcotθ = 1]
| ⇒ h2 = | 8 |
| ⇒ h = | metre | 2√2 |
