Question 374317
Notice that when you do as the problem instructs, you form a right triangle whose hypotenuse is the plank (25ft.) and whose base is the distance from the bottom of the plank to the side of the barn (7ft.).
The hypotenuse (labeled c) and the base (labeled b) can be used as b and c in the Pythagorean theorem. The height reached by the top of the plank will be repesented by a:
{{{c^2 = a^2+b^2}}} Substitute c = 25 and b = 7.
{{{25^2 = a^2+7^2}}} Simplify.
{{{625 = a^2+49}}} Subtract 49 from both sides
{{{576 = a^2}}} Finally, take the square root of both sides.
{{{24 = a}}}
The plank will reach exactly 24 feet up the barn wall.