 Hello and welcome to the session. The given question says, from an aeroplane vertically above a straight horizontal plane, the angles of deplation of two consecutive kilometers tones on opposite sides of the aeroplane are found to be alpha and beta. Show that the height of the aeroplane is tan alpha into tan beta divided by tan alpha plus tan beta. Let's start with the solution and in this figure, let A be the position of the aeroplane which is 8 meters above the plane and from here, the angle of deplation of two stones P and P was alpha and beta respectively. So this implies angle A, P, M is also alpha. Since we have drawn a line parallel to P cube from this point A, so this implies this angle is equal to this angle since these are alternating interior angles. Similarly, angle beta is equal to angle A cube M which is also equal to beta. Now, also we are given that the stones are 1 kilometers apart. So let the distance be M, take it as x kilometers. So this implies M cube is 1 minus x kilometers since P cube is whole 1 kilometers. So let us write down, we are given that P cube is equal to 1 kilometers and let P m is equal to x kilometers. So this implies that M cube is equal to 1 minus x kilometers and let the aeroplane is h meters above the ground. So we have to show that h is equal to alpha into tan beta divided by tan alpha plus tan beta. Now let us consider triangle A, P, M. In triangle A, P, M, A, M divided by P, M is equal to tan alpha. So this implies that h divided by x is equal to tan alpha or we have x is equal to h divided by tan alpha. Let this be equation number 1. Now let us consider triangle A, M cube and this triangle A, M divided by M cube is equal to tan beta and A, M is h and M cube is 1 minus x and this is equal to tan beta. This further implies that h is equal to 1 minus x into tan beta. Now on substituting x is equal to h divided by tan alpha here, this can further be written as 1 minus h divided by tan alpha into tan beta and this is from equation number 1. Now this further implies that h plus h into tan beta divided by tan alpha is equal to tan beta or we have h into tan alpha plus tan beta divided by tan alpha is equal to tan beta or we have h is equal to tan alpha into tan beta divided by tan alpha plus tan beta. This is what we have to show. Thus, of the aeroplane above the ground is tan alpha into tan beta whole divided by tan alpha plus tan beta. So, this completes the session. Bye and take care.