Answer: [tex]7\sqrt{2}[/tex] feet
Step-by-step explanation:
This question uses special right triangles.
There are two main special triangles to remember.
Attached is a diagram of the triangle. Both the base and the height are the same, so the 14 foot-long ladder is the hypotenuse.
The hypotenuse of a 45-45-90 triangle is equal to [tex]\sqrt{2} *k[/tex], where k is the side length.
We can solve for the side lengths by using this equation:
[tex]14 = \sqrt{2} *k[/tex]
Simplifying this equation by dividing both sides by the square root of 2 and rationalizing the denominator, we get
[tex]7\sqrt{2} =k[/tex]
Your side length of the height of the triangle is equal to 7 times the square root of 2.
