A ladder is leaning against a building so that the distance...

Name: Problem 25, Chapter 6: Beginning and Intermediate Algebra
Uploaded: 2020-06-09T16:46:48-08:00
Duration: 5 min 7 s
Channel: Meredith Moody
Description: A ladder is leaning against a building so that the distance from the ground to the top of the ladder is one foot less than the length of the ladder. Find the length of the ladder if the distance from the bottom of the ladder to the building is 5 feet.

A ladder is leaning against a building so that the distance from the ground to the top of the ladder is one foot less than the length of the ladder. Find the length of the ladder if the distance from the bottom of the ladder to the building is 5 feet.

Key Concepts

Right Triangle Geometry

Right triangle geometry deals with triangles that have a 90-degree angle. This concept is crucial in solving problems where one can apply specific properties, such as the relationships among the sides of the triangle, which is the groundwork for using the Pythagorean theorem in spatial problems.

Pythagorean Theorem

The Pythagorean theorem is a fundamental principle in geometry stating that for a right triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides. This theorem is essential for setting up relationships between distances in problems involving right triangles.

Quadratic Equations

Quadratic equations are polynomial equations of the second degree that often arise when algebraic relationships, set up from geometric theorems like the Pythagorean theorem, are simplified. Solving these equations is key to finding unknown variables in problems that require the formulation and solution of an equation involving squares of unknown quantities.

Transcript

00:01 I have a pythagorean theorem problem here because i have a ladder.

00:06 This is my ladder.

00:07 I'm sorry, my ladder is really, well, this isn't an art video.

00:14 That's all i mean i say.

00:15 But my ladder is leaning against a building, and that means that this is a right angle.

00:21 And because this is a right angle and the ladder makes a triangle with the ground in the building, that makes us a right triangle.

00:28 So this is a pythagorean theorem problem, which i have the formula for the pythagorean theorem up here, a squared plus b squared equals c squared.

00:36 And i know that my c squared is my hypotenuse, which is the leg or the side across from the right angle.

00:44 And so i know that the l, the latter height, is my hypotenuse.

00:50 So i'm going to rewrite this c with my l.

00:55 That's what i'm going to use l instead of c because that's the ladder.

00:59 And then so one of the other legs of the triangle is my a and one is my b.

01:05 I am going to use the a as the ground, which the ground distance between the bottom of the letter and the building as five feet.

01:16 So i'm going to substitute that in for a and that's five squared.

01:21 Then i'm going to substitute my b side, my b leg as l minus 1 because i know that this height of where the, not the height of the ladder, but where the ladder is tilting against the building, how high it is from the bottom of the building to the ladder is one foot less than the ladder.

01:51 Or the length of the latter.

01:52 So we have l minus 1 squared.

01:55 So now i'm going to sort of work with my variables here.

02:00 So i am going to have 5 squared.

02:04 I mean, that's my constant.

02:06 So i'm going to simplify that or perform that operation there.

02:10 And then i'm going to foil my l minus 1.

02:17 And then i have l squared here.

02:19 So i have 25 plus.

02:21 My first which l times l is l squared my outer which is l times negative one which is me negative l my inner which is l times negative one which gives me negative l and my last sorry i should have written i there and my last which is negative one times negative one which is positive one equals l squared so now i'm going to combine these like terms here so i get 25 plus l squared minus 2l plus 1 equals l squared...

Please give Ace some feedback