Question 39565
a.Find the length of a rectangle whose diagonal is 10in. and whose width is 7in.
Imagine half of the rectangle as a right triangle: {{{c^2 = a^2 + b^2}}}
{{{10^2 = 7^2 + b^2}}}
{{{100 = 49 + b^2}}}
{{{51 = b^2}}}
{{{sqrt(51) = b}}} about 7.141 inches
b. The base of a 15-ft ladder is 5 ft away from a wall. How far above the floor is the top of the ladder?
It depends on the location of the floor. I will solve using the idea of the floor's location at the wall. You should imagine this. You see a right triangle forming again.
{{{15^2 = 5^2 + b^2}}}
{{{225 = 25 + b^2}}}
{{{200 = b^2}}}
{{{b = sqrt(200)}}} about 14.142 feet