Trigonometry » Tangent

The following formula is for the tangent:
tan(angle signA) = opposite shorter side of angle signAadjacent shorter side of angle signA

Check opposite and adjacent side if you need more information about this.


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(angle sign...) = 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 angle signA, round your answer to
one decimal.

Answer:
2. tan(angle signA) = oa
3. tan(angle signA) = 103
4. angle signA = tan-1(103) ≈ 73.3° 
Triangle with adjacent 3 and opposite 10

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 angle signB = 20°, angle signC = 90° and BC = 10 m.
Calculate the length of AC, round your answer to one decimal.

Answer:

1. Draw a sketch first.
Triangle with angle 20° and adjacent 10
2. tan(angle signB) = 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 angle signA = 68°, angle signC = 90° and BC = 8.5 m.
Calculate the length of AC, round your answer to one decimal.

Answer:

1. Draw a sketch first.
Triangle with angle 68° and opposite 8.5
2. tan(angle signA) = 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

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 8.5 : tan 68.