 Hi and welcome to the session. Let us discuss the following question which says in figure A D is equal to 4 centimeters, B D is equal to 3 centimeters and C B is equal to 12 centimeters. Find cot theta. Before moving on to the solution let's recall that for any angle theta cot theta is given by base upon perpendicular. This is the key idea that we will use for this question. Now let's move on to its solution. First of all let us see what is given to us in the question. We are given that A D is equal to 4 centimeters, B D is equal to 3 centimeters, C B is equal to 12 centimeters and we need to find cot theta. Now here angle A C B is given to be theta, angle A B C is a right angle and angle A D B is also a right angle. So that means triangle A B C and triangle A D B are right angle to triangles. So first of all consider the right angle to triangle A D B. So in right triangle A D B angle A D B is a right angle that means A B is the hypotenuse. So we have A B square is equal to A D square plus B D square by Pythagoras theorem. Now let us substitute the values of A D and B D. So this implies A B square is equal to A D square that is 4 square plus B D square that is 3 square centimeter square which is equal to 16 plus 9 centimeter square that is 25 centimeter square. Thus A B will be equal to 5 centimeters. So here we have A B equal to 5 centimeters. Now consider the triangle A B C. So in right triangle A B C we know that cot theta is equal to base upon perpendicular. So that means here cot theta will be equal to base that is B C upon perpendicular that is A B which will be equal to 12 upon 5. Thus cot theta is equal to 12 upon 5 is the required answer to this question. With this we finish this session. Hope you must have understood the question. Goodbye, take care and have a nice day.