Right-triangle trigonometry, step by step

Once a triangle has a right angle, one more angle or one more side pins down the rest.

The question
611x degrees

Find the angle: opposite 11, adjacent 6

tan x=11 ÷ 6
x=tan⁻¹(11 ÷ 6)
x=61°
  1. You know the two legs: the side opposite the angle is 11, and the side next to it (adjacent) is 6. Opposite over adjacent is the tangent.
  2. To undo the tangent, use inverse tangent (tan⁻¹ on the calculator): x = tan⁻¹(11 ÷ 6).
  3. That is 61° to the nearest degree.

How it works.

  1. 01

    You know the two legs: the side opposite the angle is 11, and the side next to it (adjacent) is 6. Opposite over adjacent is the tangent.

  2. 02

    To undo the tangent, use inverse tangent (tan⁻¹ on the calculator): x = tan⁻¹(11 ÷ 6).

  3. 03

    That is 61° to the nearest degree.