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Trigonometric Ratios with a Calculator

Solving for values when triangles aren't special right triangles.

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Trigonometric Ratios with a Calculator

Trigonometric Ratios with a Calculator

There is a fixed sine, cosine, and tangent value for every angle, from to . Your scientific (or graphing) calculator knows all the trigonometric values for any angle. Your calculator, should have [SIN], [COS], and [TAN] buttons. You can use your calculator and the trigonometric ratios is to find the missing sides of a right triangle by setting up a trig equation.

What if you were given a 20-70-90 triangle? How could you find the sine, cosine, and tangent of the and angles?

 

Examples

Example 1

Find the length of the missing sides and round your answers to the nearest tenth:

Use tangent for and cosine for .

Example 2

Find the length of the missing sides and round your answers to the nearest tenth:

Use tangent for and cosine for .

Example 3

Find the trigonometric values, using your calculator:

,

Round to 4 decimal places.

Depending on your calculator, you enter the degree and then press the trig button or the other way around. Also, make sure the mode of your calculator is in DEGREES.

 

 

 

Example 4

Find the value of each variable. Round your answer to the nearest tenth.

We are given the hypotenuse. Use sine to find , and cosine to find . Use your calculator to evaluate the sine and cosine of the angles.

Example 5

Find the value of each variable. Round your answer to the nearest tenth.

We are given the adjacent leg to . To find , use cosine and use tangent to find .

Any time you use trigonometric ratios, use only the information that you are given. This will result in the most accurate answers.

Review

Use your calculator to find the value of each trig function below. Round to four decimal places.

Find the length of the missing sides. Round your answers to the nearest tenth.

Review (Answers)

To see the Review answers, open this PDF file and look for section 8.8. 

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Vocabulary

trigonometry

The study of the relationships between the sides and angles of right triangles.

Hypotenuse

The hypotenuse of a right triangle is the longest side of the right triangle. It is across from the right angle.

Legs of a Right Triangle

The legs of a right triangle are the two shorter sides of the right triangle. Legs are adjacent to the right angle.

Trigonometric Ratios

Ratios that help us to understand the relationships between sides and angles of right triangles.

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