# Trigonometry » Tangent

The following formula is for the tangent:
t`an`(A) = opposite shorter side of Aadjacent shorter side of A

## How do you use the tangent?

Use the following plan/steps/method:

1. Draw a sketch if it is not yet given.
2. Write down the rule: `tan`(...) = oa.
3. Fill in the data that is given.
4. Calculate the unknown value. If necessary, use  2 = 63.

## Example 1: Calculate an angle

 Question: Calculate A, round your answer to one decimal. Answer: 2. `tan`(A) = oa 3. `tan`(A) = 103 4. A = `tan`-1(103) ≈ 73.3°

Note to step 4:
- On your calculator, you do: [2nd] or [shift] `tan` (10 : 3) ≈ 73.301
- Sometimes `arctan` has to be used instead of `tan`-1.

## Example 2: Calculate a side

Question:
Given is triangle ABC with B = 20°, C = 90° and BC = 10 m.

 1. Draw a sketch first.
 2. `tan`(B) = oa
 3. `tan`(20°) = ?10
 4. Use 2 = 63 The ? is at the location of the 6. To get 6, you have to do 2 × 3. Looking back to step 3, we have to do `tan`(20°) × 10. AC = `tan`(20°) × 10 ≈ 3.6 m

Note to step 4:

 - You do not have to key in the °-sign on the calculator. - Some calculators do not automatically put a '(' behind `tan`.If you want you can just key in `tan` 20 × 10.

## Example 3: Calculate a side

Question:
Given is triangle ABC with A = 68°, C = 90° and BC = 8.5 m.
 2. `tan`(A) = oa
 3. `tan`(68°) = 8.5?
 4. Use 2 = 63 The ? is at the location of the 3. To get 3, you have to do 6 : 2. Looking back to step 3, we have to do 8.5 : `tan`(68°). AC = 8.5 : `tan`(68°) ≈ 3.4 m
 - You do not have to key in the °-sign on the calculator. - Some calculators do not automatically put a '(' behind `tan`.If you want you can just key in 8.5 : `tan` 68.