Find the coordinates of the centroid of the triangle with the given vertices. S(5, 5), T(11, -3), U(-1, 1)

Arandom high school question but a hard one

A20? -foot ladder is placed against a vertical wall of a? building, with the bottom of the ladder standing on level ground 19 feet from the base of the building. how high up the wall does the ladder? reach?

Arley is building a model of a city map. in one part of the city, three roads form a right triangle, which harley draws as triangle abc, with the following measures: m∠b=90° and m∠a=30°. in his scale model, the hypotenuse of triangle abc, ac¯¯¯¯¯¯¯¯, has a length of 817−−√ cm. what is the value of a (the length of bc¯¯¯¯¯¯¯¯)?