 Hi friends, I am Purva and today we will discuss the following question. A boy standing on horizontal plane finds a bird flying at a distance of 100 meters from him at an elevation of 30 degrees. A girl standing on the roof of 20 meter high building finds the angle of elevation of the same bird to be 45 degrees. Both the boy and the girl are on opposite sides of the bird. Find the distance of bird from the girl. Let us begin with the solution now. Now let the bird be at the point A. The boy is at the point P on the ground and the girl is at point Q with just 20 meters above the ground. Therefore we have A P is equal to 100 meters, Q D is equal to 20 meters, angle A Q C is equal to 45 degrees, angle A P B is equal to 30 degrees. Now in right angle triangle A B P we have A B upon A P is equal to sign 30 degrees because we know that sin theta is equal to perpendicular upon hypotenuse. Now in this triangle A B P we know that perpendicular is A B and hypotenuse is A P. So we get A B upon A P is equal to sign 30 degrees. That is we have A B upon A P. Now A B is equal to 100 meters. So we have A B upon 100 is equal to sign 30 degrees which is equal to 1 upon 2. Or we can say A B is equal to 100 upon 2 which is equal to 50 meters. So we have got A B is equal to 50 meters. Now we have to find the distance of the bird from the girl that is we have to find A Q. Now since we have A B is equal to 50 meters therefore A C is equal to A B minus C B. This is equal to A B minus Q D because we have C B is equal to Q D and this is equal to 50 minus 20 because we know that A B is equal to 50 meters and Q D is equal to 20 meters. And so we get A C is equal to 50 minus 20 that is 30 meters. Now in right angle triangle A C Q we have perpendicular upon hypotenuse is equal to sign theta. That is we have A C upon A Q is equal to sign 45 degrees. Or we have now A C is equal to 30 meters so we have 30 upon A Q is equal to sign 45 degrees which is equal to 1 upon root 2 or A Q is equal to 30 root 2 meters. Hence the bird is 30 root 2 meters away from the girl. So we have got our answer as 30 root 2 meters. Hope you have understood the solution. Bye and take care.