The ladder reaches about 9.5 feet up the wall. Try to visualize the ladder in your head, and you will see that it forms a right triangle. Since it's a right triangle, we can use the Pythagorean Theorem to find the missing length. The ladder itself is the hypotenuse, while its distance from the wall and its height up the wall are the triangle's two legs.
a² + b² = c² Pythagorean Theorem
3² + b² = 10² Plug in your values. Since 3 is the length of one of the legs, it can be either a or b. Since the ladder's length, 10, is the hypotenuse, it is c.
9 + b² = 100 Exponents (3² = 9, 10² = 100)
b² = 91 Subtract 9 from 100 to isolate b²
b = √91 Take the square root of both sides to cancel out the exponent
Therefore, the correct answer is about 9.5 feet, or √91 feet.
Hope this helps!
