Can you use sine and cosine law on right triangles?
The Sine Rule can be used in any triangle (not just right-angled triangles) where a side and its opposite angle are known. You will only ever need two parts of the Sine Rule formula, not all three. You will need to know at least one pair of a side with its opposite angle to use the Sine Rule.
Yet trigonometry—a subject whose rules are generally based on right triangles—can still be used to solve a non-right triangle. You need different tools, though. Enter the laws of sines and cosines. In an oblique triangle, there are six unknowns: the three angle measures and the three side lengths.
- In this right triangle, you are given the measurements for the hypotenuse, c, and one leg, b. The hypotenuse is always opposite the right angle and it is always the longest side of the triangle. To find the length of leg a, substitute the known values into the Pythagorean Theorem.
- Law of Cosines. The law of cosines for calculating one side of a triangle when the angle opposite and the other two sides are known. Click on the highlighted text for either side c or angle C to initiate calculation.
- In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of a triangle (any shape) to the sines of its angles. It can also be used when two sides and one of the non-enclosed angles are known.
The trigonometric functions are based on a measure of 90 degrees yes, but it is not restricted to work with only right triangles. You can use sine and cosine laws when the triangle isn't a right triangle.
- The Law of Sines says that in any given triangle, the ratio of any side length to the sine of its opposite angle is the same for all three sides of the triangle. This is true for any triangle, not just right triangles. Press 'reset' in the diagram above.
- "SSS" is when we know three sides of the triangle, and want to find the missing angles. To solve an SSS triangle: use The Law of Cosines first to calculate one of the angles. then use The Law of Cosines again to find another angle.
- The Law of Sines is the relationship between the sides and angles of non-right (oblique) triangles . Simply, it states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in a given triangle.
Updated: 3rd September 2018