How to Calculate Compound Angles

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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.

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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.

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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.

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