Chapter 0.8, Problem 18E

To determine

Application problem involves right triangles and the Pythagorean Theorem with necessary diagrams.

Answer to Problem 18E

For the assumed situation,the ladder reaches 8 ft. up the side of house.

Explanation of Solution

Given information:

Right triangles:

Area,

  $A=\frac{1}{2}\times b\times h$

Pythagorean Theorem:

  $b^2+h^2=H^2$

Where,

b : Base

h : Height

H : Slant height

Assume a simple situation:

John’s ladder is 10 ft. long, it is placed 6 ft. away from his house.

Now,

Find the height at which it will reach.

First of all,

Draw the diagram:

  

Use Pythagorean Theorem to solve for x :

  $b^2+h^2=H^2$

Substitute values:

  ${\left(6\right)}^2+{\left(x\right)}^2={\left(10\right)}^2$

That becomes

  $36+x^2=100$

The further becomes

  $x^2=64$

Thus,

  $x=\sqrt{64}=8$

The ladder reaches 8 ft. up the side of house.