A pole stands vertically in the center of a square. When 45 o is the elevation of the sun, the tip of its shadow just reaches the side of the square and is at a distance of 30 meters and 40 meters from the ends of that side. The height of the pole is

Step-by-step solution

Let A B C D is a square and O P is the pole. Now, ∠ P Q O = 45 o Also, D Q = 30 meters Q A = 40 meters Side of square = 30 + 40 = 70 meters Now in ∆ P O Q , ∠ Q = 45 o and ∠ O = 90 o ∴ ∠ P = 45 o ∴ O P = O Q = h (let) Now, let a perpendicular is drawn from O to A D which is O M In ∆ O M Q , Q M = D M - Q D = 70 2 - 30 = 5 meters O M = A B 2 = 70 2 = 35 meters ∴ O Q = Q M 2 + O M 2 = 5 2 + 35 2 = 5 1 + 7 2 = 25 2 meters