Geometry Question ..... kindly answer the question in the description. Thanks

Question

Jules needs to purchase a ladder that just reaches the top of a 16-foot building. If the bottom of the ladder will be placed 12 feet from the base of the building, how long should Jule's ladder be?

Answer 1

Many, many book problems, homework problems, and test problems have "Pythagorean Triples" of:

     n*1      n*1        n*√2

     n*1      n*√3      n*2

     n*3      n*4         n*5

  ...

 

Also, the angles of each of these triangles are well-known.  So, learning them will save you a lot of time.

 

The ground leg is 4*3; the height of the building is 4*4; so the hypotenuse (the ladder) must be 4*5=20.

 

Calculate that using the Pythagorean Theorem once, then use that information to check your answer, then to solve problems very quickly.

Answer 2

When a ladder leans leans against a building it forms a right triangle with the side of the building and the ground.  In this case, the ladder is the hypotenuse and the side of the building and the ground are the legs.

 

Since the ladder is 12 feet away from the building, one leg (a) is 12.

Since the ladder needs to reach a height of 16 feet, the other leg (b) is 16.

 

Remember, the Pythagorean Theorem states that the sides of a right triangle where c is the hypotenuse have the relationship of a²+b²=c².

 

Therefore, in your problem:

 

12²+16²=c²

144+256=c²

400=c²

20=c

 

The ladder needs to be 20 feet long.