Verify that 1 + cot2 x = csc2 x is an identity.

Aman is 6 feet 3 inches tall. the top of his shadow touches a fire hydrant that is 13 feet 6 inches away. what is the angle of elevation from the base of the fire hydrant to the top of the man's head?

Bob is putting books on a shelf and takes a break after filling 18 1/2 inches on the book shelf. the book shelf is now 2/3 full. how long is the entire bookshelf?

Asquare and an equilateral triangle have the same perimeter. each side the triangle is 4 inches longer than each side of the square. what is the perimeter of the square