A tower subtends an angle 75 o at a point on the same level as the foot of the tower and at another point, 10 meters above the first, the angle of depression of the foot of the tower is 15 o . The height of the tower is (in meters)

Step-by-step solution

From the figure, in right-angled ∆ A B D , A B B D = tan ⁡ 75 o ∴ h x = tan ⁡ 75 o ⇒ h = x tan ⁡ 75 o … … . . i In right-angled ∆ B C E , B E E C = tan ⁡ 15 o ⇒ 10 x = tan ⁡ 15 o ∴ x = 10 tan ⁡ 15 o … … i i From i and i i , we get, ∴ h = 10 tan ⁡ 15 o × tan ⁡ 75 o = 10 2 + 3 2 meters