# Trigonometry » Cosine

The following formula is for the cosine:
c`os`( A) = adjacent shorter side of Ahypotenuse

## How do you use the cosine?

Use the following plan/steps/method:

1. Draw a sketch if it is not yet given.
2. Write down the rule: `cos`( ...) = ah.
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. `cos`( A) = ah 3. `cos`( A) = 310 4. A = `cos`-1(310) ≈ 72.5° Note to step 4:
- On your calculator, you do: [2nd] or [shift] `cos` (3 : 10) ≈ 72.542...
- Sometimes `arccos` has to be used instead of `cos`-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. `cos`( B) = ah
 3. `cos`(20°) = 10?
 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 10 : `cos`(20°). AB = 10 : `cos`(20°) ≈ 10.6 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 `cos`.If you want you can just key in 10 : `cos` 20.

## Example 3: Calculate a side

Question:
Given is triangle PQR with P = 24°, Q = 90° and PR = 42.
 1. Draw a sketch first. 2. `cos`( P) = ah
 3. `cos`(24°) = ?42
 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 `cos`(24°) × 42. QR = `cos`(24°) × 42 ≈ 38.4 m
 - You do not have to key in the °-sign on the calculator. - Some calculators do not automatically put a '(' behind `cos`.If you want you can just key in `cos` 24 × 42.