How To Calculate Compound Angles
Things Needed
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Pencil
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Paper
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Ruler or tape measure
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Calculator or spreadsheet software
Tip
When angles A and B are equal, you can use the double angle formula. Simply substitute A for B in the compound angle formula to get the double angle formula: sin2A = 2sinAcosA.
You can use these steps to calculate any compound angle by making two right triangles from the angles A and B using drawn lines or string.
When cutting compound wood angles, such as on rafters, you can use the compound angle formula to calculate the angles before you cut.
A compound angle is an angle made by two angles. Compound angles can be calculated when you know all the sides of two right triangles that form the compound angle. Five simple trigonometry formulas are used.
Calculation Instructions
Step 1
Measure the three sides for each of two right triangles that form the compound angle. For the triangle with angle A, use the ruler or tape measure to measure adjacent side a, opposite side a and hypotenuse a. For the triangle with angle B, measure adjacent side b, opposite side b and hypotenuse b. Record the six side length measures on a sheet.
Step 2
Calculate the sine and cosine for angle A. Use the two formulas sine A = opposite side a/hypotenuse a and cosine A = adjacent side a/hypotenuse a.
Step 3
Calculate the sine and cosine for angle B. Use the two formulas; sine B = opposite side b/hypotenuse b and cosine B = adjacent side b/hypotenuse b.
Step 4
Calculate the compound angle A+B. Substitute the sine and cosine for angle A and sine and cosine for angle B in the compound angle formula. The compound angle formula is: sin(A+B) = sinAcosB + cosAsinB. The substitution produces the formula: sin(A+B) = (opposite side a/hypotenuse a)(adjacent side b/hypotenuse b) + (adjacent side a/hypotenuse a)(opposite side b/hypotenuse b). Use the calculator to take the inverse sine of the sum of the two products to find the compound angle A+B.