Finding a missing side, step by step

With a right triangle, one angle and one side are enough to find any other side — through sine, cosine or tangent.

The question
x565° cm

Find the opposite, angle 65°

opposite ÷ hypotenuse=sine
sin 65° = x ÷ 5
x=4.5
  1. The angle is 65°. You know the hypotenuse (5) and you want the opposite (x). Those two sides are the opposite and the hypotenuse, so the ratio is the sine.
  2. Write it with the numbers: sin 65° = x ÷ 5.
  3. Rearrange for x and work it out on a calculator: x = 5 × sin 65° = 4.5.

How it works.

  1. 01

    The angle is 65°. You know the hypotenuse (5) and you want the opposite (x). Those two sides are the opposite and the hypotenuse, so the ratio is the sine.

  2. 02

    Write it with the numbers: sin 65° = x ÷ 5.

  3. 03

    Rearrange for x and work it out on a calculator: x = 5 × sin 65° = 4.5.