# Building a dog house on the side of a shed.

1. Apr 8, 2009

### Zombie Acorn

First post here, although I could eyeball this project I have been stumped as to how it would be calculated. I haven't been in a geometry class for nearly a decade so this really brought to light how much I have forgot. I need to find how tall a board would be cut if it descends at a certain slope for x amount of feet assuming the ground is level. I drew a diagram, basically I need to know how to solve for x, but I would like to know how it is done. Thanks for any help.

EDIT: FORGOT TO MENTION IN MY DIAGRAM THAT THE ROOF PIECE THAT IS SLOPING IS 4 FT LONG, I IMAGINE THAT IS IMPORTANT.

2. Apr 8, 2009

### HallsofIvy

Staff Emeritus
So then, your board is sloping, at a 15 degree angle, from 3 feet to x feet? Drawing a perpendicular from the end of the "roof" to the wall gives a right triangle with angle 15 degrees and "opposite side" 3- x feet. You want to find the length of the hypotenuse of that triangle. Since sin(a) is defined as "opposite side divided by hypotenuse", hypotenuse equals opposite side divided by sin(a): the length is (3-x)/sin(15).