Worked example

Two lines have slopes 3 and 1/2. What is the tangent of the angle between them?

Steps

1. slope = tan of inclination
   tan A = 3, tan B = 1/2.
2. tan(A − B) = (tan A − tan B)/(1 + tan A tan B)
   Tangent of a difference. · Tangent of a difference
3. = (3 − 1/2)/(1 + 3/2)
   Substitute.
4. = (5/2)/(5/2) = 1
   So A − B = 45°.

Identities used

• Tangent of a difference — Angle between two lines with slopes m₁ and m₁: set tan A = m₁, tan B = m₂ and this formula gives the tangent of the angle between them.

Check it yourself

Open the verifier with the main identity pre-filled — substituting your own numbers into a step is the fastest way to find out which line you did not follow.

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