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
cm
Find the opposite, angle 65°
opposite ÷ hypotenuse=sine
sin 65° = x ÷ 5
x=4.5
- 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.
- Write it with the numbers: sin 65° = x ÷ 5.
- Rearrange for x and work it out on a calculator: x = 5 × sin 65° = 4.5.
How it works.
- 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.
- 02
Write it with the numbers: sin 65° = x ÷ 5.
- 03
Rearrange for x and work it out on a calculator: x = 5 × sin 65° = 4.5.