A book that is 13 in. tall is leaning against the edge of a wall. If the bottom of the book is 5 inches from the wall, how far up the wall is the top of the book?
are you familiar with the 5-12-13 right triangle?
No
To find out how far up the wall the top of the book is, we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the distance up the wall (let's call it "x") represents one side of the triangle, the distance from the bottom of the book to the wall (5 inches) is the second side, and the height of the book (13 inches) is the hypotenuse.
Using the Pythagorean Theorem, we have:
x^2 + 5^2 = 13^2
Simplifying this equation:
x^2 + 25 = 169
Subtracting 25 from both sides:
x^2 = 144
Taking the square root of both sides:
x = √144
Therefore, x = 12.
So, the top of the book is 12 inches up the wall.