Atower casts a shadow 11 feet long. the distance from the top of the tower to the end of the shadow is 61 feet. how many feet tall is the tower?

If you draw out the diagram, you should have a right triangle, where the height of the triangle is how tall the tower is ( x ), the base is the length of the shadow (11), and the distance from the top of the tower to the end of the shadow is the hypotenuse (61). 

the pythagoreon theorem states that for any right triangle:
a² + b² = c² 

a is side 1, b is side 2, and c is the hypotenuse. 
Knowing this, we can plug in the values 11 and 61. 

11² + b² = 61²
121 + b² = 3721
b² = 3600
b = 60 

The tower is 60 feet tall.