# Trigonometry » Sine

The following formula is for the sine:
s`in`( A) = opposite shorter side of Ahypotenuse

## How do you use the sine?

Use the following plan/steps/method:

1. Draw a sketch if it is not yet given.
2. Write down the rule: `sin`( ...) = oh.
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. `sin`( A) = oh 3. `sin`( A) = 4.27.0 4. A = `sin`-1(4.27.0) ≈ 36.9° Note to step 4:
- On your calculator, you do: [2nd] or [shift] `sin` (4.2 : 7.0) ≈ 36.869...
- Sometimes `arcsin` has to be used instead of `sin`-1.

## Example 2: Calculate a side

Question:
Given is triangle PQR with P = 22°, Q = 90° and PR = 4.

 1. Draw a sketch first. 2. `sin`( P) = oh
 3. `sin`(22°) = ?4
 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 `sin`(22°) × 4. QR = `sin`(22°) × 4 ≈ 1.5 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 `sin`.If you want you can just key in `sin` 22 × 4.

## Example 3: Calculate a side

Question:
Given is triangle ABC with A = 68°, C = 90° and BC = 8.5 m.
 1. Draw a sketch first. 2. `sin`( A) = oh
 3. `sin`(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 : `sin`(68°). AB = 8.5 : `sin`(68°) ≈ 9.2 m
 - You do not have to key in the °-sign on the calculator. - Some calculators do not automatically put a '(' behind `sin`.If you want you can just key in 8.5 : `sin` 68.