Question

If A = 60° and B = 30°, verify that : sin (A + B) = sin A cos B + cos A sin B

A pole 6m high is fixed on the top of a tower. The angle of elevation of the top of the pole observed from a point P on the ground is 60° and the angle of depression of the point P from the top of the tower is 45°. Find the height of the tower and the distance of point P from the foot of the tower. (Use √3 = 1.73)

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 :

It is given that sin (A − B) = sin A cos B − cos A sin B. Use it to find the value of sin 15°.