Answer:
20.62
Step-by-step explanation:
In this instance, we are going to use the pythagorean theorem.
The height of the gutter will be a leg of the triangle, and the ladder will be the hypotenuse. The formula is
[tex]a^{2} + {b}^{2} = {c}^{2} [/tex]
While A and B are legs and C is the hypotenuse. We are trying to find B, the distance from the house.
So plug A and C in:
[tex] {40}^{2} + {b}^{2} = {45}^{2} [/tex]
Now figure it out: first you square 40 and 45:
[tex]1600 + {b}^{2} = 2025[/tex]
Isolate the B term: subtract 1600 from both sides
[tex] {b}^{2} = 425[/tex]
Now take the square root of both sides to find B
[tex]b = 20.62[/tex]
And that's your answer
