The angle of elevation of the top of a tower from a point A due north of it is α and from a point B at a distance of 9 units due west of A is cos - 1 3 13 . If the distance of the point B from the tower is 15 units, then cot α is equal to

Step-by-step solution

Given, The angle of elevation of the top of a tower from a point A due north of it is α and from a point B at a distance of 9 units due west of A is cos - 1 3 13 . If the distance of the point B from the tower is 15 units, then cot α is equal to Now making the diagram of given value we have, Given O B = 15 cos β = 3 13 So, tan β = 2 3 Now using the value of tan β in △ O P B we get, ⇒ tan β = h 15 ⇒ 2 3 = h 15 , so h = 10 Now in △ O A B O A 2 + A B 2 = 225 &#8658