If from the top of a tower 80 meters high the angles of depression of the top and bottom of a house are 30 o and 45 o respectively, then the height of the house is

Step-by-step solution

Let, O A is tower and B C is house Given, O A = 80 meters ∠ A C D = 30 o ∠ A B O = 45 o Let, B C = h meters In Δ A B O , OA OB = tan ⁡ 45 o ⇒ OB = 80 tan ⁡ 45 o = 80 meters In Δ A D C , AD DC = tan ⁡ 30 o O A - O D O B = 1 3 ∵ O B = D C 80 - h 80 = 1 3 80 3 - 3 h = 80 ⇒ h = 80 3 - 1 3 meters