The pta created a cross country trail for the meet. the pta placed a trail marker in the ground every four hundred years. every nine hundred years the pta set up a water station. what is the shortest distance a runner will have to run to see both a water station and trail marker at the same location?

How to choose the sign of the radical in the denominator of the formula for the distance from a point to a line.

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¯¯¯¯¯¯¯¯)?

One side of a rectangle is 7 feet shorter than seven times the other side. find the length of the shorter side if we also know that the perimeter of the rectangle is 306 feet.