Question

The Statue of Unity situated in Gujarat is the world's largest Statue which stands over a 58 m high base. As part of the project, a student constructed an inclinometer and wishes to find the height of Statue of Unity using it. He noted following observations from two places : Situation – I : The angle of elevation of the top of Statue from Place A which is 80√3 m away from the base of the Statue is found to be 60°. Situation – II : The angle of elevation of the top of Statue from a Place B which is 40 m above the ground is found to be 30° and entire height of the Statue including the base is found to be 240 m. Based on given information, answer the following questions :

If x = cos 30° – sin 30° and y = tan 60° – cot 60°, then

If x = 2 sin 60° cos 60° and y = sin²30° − cos²30° and x² = ky², the value of k is

An observer 1.8 m tall stands away from a chimney at a distance of 38.2 m along the ground. The angle of elevation of top of chimney from the eyes of observer is 45°. The height of chimney above the ground is