URGENT PLEASE HELP If you answer this correctly ill answer some of your questions you have posted! (29pts)

The depth of a lake at a certain point, wich is a function of the distance of that point from shore, is 30 feet.

If tan2a=cot(a+60), find the value of a, where 2a is an acute angle

Prove the converse of the pythagorean theorem using similar triangles. the converse of the pythagorean theorem states that when the sum of the squares of the lengths of the legs of the triangle equals the squares length of the hypotenuse, the triangle is a right triangle. be sure to create and name the appropriate geometric figures.