What if you were given a 20-70-90 triangle? How could you find the sine, cosine, and tangent of the and angles? After completing this Concept, you'll be able to use a calculator to find the trigonometric ratios for angles that do not measure , , or .

### Watch This

CK-12 Foundation: The Trigonometric Ratios with a Calculator

James Sousa: Determining Trigonometric Function Values on the Calculator

### Guidance

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.

#### Example A

Find the trigonometric value, using your calculator. Round to 4 decimal places.

a)

b)

c)

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.
*

a)

b)

c)

#### Example B

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 C

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.

CK-12 Foundation: The Trigonometric Ratios with a Calculator

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### Guided Practice

1. What is ?

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

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

**
Answers:
**

1. Using your calculator, you should find that ?

2. Use tangent for and cosine for .

3. Use tangent for and cosine for .

### Explore More

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.