We are given that the bottom of a 13-foot ladder stands 5 feet from the house and from the top of the ladder we can reach another 4 feet safely.
Now, we want to know whether we can reach the window that is 13 feet above the ground. To do this, we have to find the length from the ground to the top of the ladder first. Let b be the missing length.
From the graph we can see that the ladder forms a right triangle with the wall and the ground. This means that we can use the Pythagorean Theorem to find b. Let's recall it!
a^2+ b^2= c^2
In the formula, a and b are the lengths of the legs and c is the length of the hypotenuse of a right triangle. In our triangle a= 5 and c= 13. Let's substitute these values into the formula.
a^2+ b^2= c^2
⇕
5^2+ b^2= 12^2
Now we can solve the equation to find the value of b.
Notice that we only consider positive solution because a side length cannot be negative.
We found that the top of the ladder is 12 feet above the ground. We know that we can safely reach the next 4 feet. Therefore, the maximum height is 12 + 4=16 feet. Let's show this on our diagram.
The maximum height that we can reach is 16 feet and the window is located 13 feet above the ground. This means that we can safely reach the window.
