Suppose a roof has a rise of 18 inches and a run of 15 feet.

How long is the rafter? Only very simple tools are needed to cut r roof rafters such as a saw, framing square or carpenters square and a tape measure.

## Finding the Right Angle | THISisCarpentry

The framing square is made up of two legs joined at the heel to form a right angle. The longer leg of the framing square is called the body and the shorter one leg is called the tongue.

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A Gable is a triangle formed by a sloping roof. A building may be front-gabled or side-gabled.

The valley formed from the two common rafters and can be thought of as the diagonal in a rectangular solid. From geometry we know that right triangles are similar therefore the sides of one triangle is proportional to the sides of the other. When the Pitch of the two intersecting roofs are not the same, see Gable picture, then the valley rafter calculation will involve a proportion.

### Getting Things Square With the World: 3-4-5 Triangles

To calculate the area of a rectangle, simply multiply the length of side 1 by the length of side 2. To calculate area of a trapezoid, multiply its height by one-half the sum of the parallel sides. To calculate the area of a circle, multiply the circumference by one-half the radius. To calculate the circumference of a circle, multiply the diameter by 3.

To calculate the volume of a cylinder, multiply the radius squared x 3.

### Finding the Right Angle

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Large remodeling and construction projects such as laying out the foundation of a house or walls often employ a triangle technique to ensure accurate 90 degree angles. No matter what project you work on if your base or foundation is not level, plumb and square the rest of you project will be off. Errors at the base of a deck, house or porch will continue to grow and compound by the time you get to the finish trim, cabinets or reach the roof framing.

If the short side of the triangle is 3 feet, and the leg that extends from it 90 degrees is 4 feet, the hypotenuse, or longest leg, will be 5 feet.

## Carpentry Math

This technique simply requires that the carpenter create a triangle in the corner of the lines that are to be square 90 degrees to each other. Any triangle with sides of 3, 4 and 5 feet will have a 90 degree angle opposite the 5 foot side. The beauty and simplicity of this technique is if the carpenter or builder needs to increase accuracy on larger walls or structures, any multiple of the rule can be deployed.

In Geometry, a well known method of constructing a right angle is to employ the Pythagorean Theorem. The mathematician, Pythagoras, discovered a relationship between the sides of any right triangle that is now known as the Pythagorean Theorem; he proved that the square of the longest side the hypotenuse is equal to the sum of the squares of the remaining two sides. A and B are the two legs of the right triangle and C is the hypotenuse.