This section uses the trigonometric ratios to find angles of right triangles. A calculator is needed.

Trigonometric ratios are used to calculate the measures of one (or both) of the acute angles in a right triangle, if you know the lengths of two sides of the triangle.

Example

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Step 1: Identify the reference angle, the adjacent leg, the opposite leg, and the hypotenuse.

Identify them in your diagram by mousing over the image below of a triangle.
Find: Adjacent Leg, Opposite Leg, Hypotenuse, and Reference Angle.

Step 2: Identify the information you are given and the information you are looking for.

• Given: ___________
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The length of the opposite leg and the hypotenuse
• Find: ___________
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m ∠ H

Step 3: Identify the trigonometric ratio that relates the two side lengths from Step 2.

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The sine ratio relates the length of the opposite leg and the length of the hypotenuse.

Step 4: Set up a ratio, including the angle measure, known side length, and unknown side length.

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sinH =  Opposite Leg Hypotenuse

sinH =  16 20

Step 5: Solve for the angle measure using the inverse trigonometric ratio. On your calculator, this can be found using the 2^nd-SIN or INV-SIN keystroke. Round the answer to the appropriate place value.

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