When you know the values for two or more sides of a triangle, you can use the law of cosines. In the following case, you know all three sides (which is called SSS, or side-side-side, in trigonometry) but none of the angles.
Is SSS Law of Sines or cosines?
Use the law of cosines when you are given SAS, or SSS, quantities. For example: If you were given the lengths of sides b and c, and the measure of angle A, this would be SAS. SSS is when we know the lengths of the three sides a, b, and c. Use the law of sines when you are given ASA, SSA, or AAS.
Is SSS the Law of Sines?
The Law of Sines is a valuable tool in solving triangles, but it requires knowing an angle and its opposite side. So, the Law of Sines cant be used as a first step in solving SSS (side-side-side) or SAS (side-angle-side) configurations.
How do you know when to use the law of sines or cosines?
The sine rule is used when we are given either a) two angles and one side, or b) two sides and a non-included angle. The cosine rule is used when we are given either a) three sides or b) two sides and the included angle.
How do you use the Law of Cosines in SSS?
0:515:19How to use law of cosines for SSS - YouTubeYouTube
Can you use the law of sines on any triangle?
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. As before, you will only need two parts of the Sine Rule , and you still need at least a side and its opposite angle.
What is the shortest side of a 30-60-90 Triangle?
And because we know that we cut the base of the equilateral triangle in half, we can see that the side opposite the 30° angle (the shortest side) of each of our 30-60-90 triangles is exactly half the length of the hypotenuse.
How do you prove a 30-60-90 Triangle?
2:403:5230-60-90 Triangle Theorem - Proof | Dont Memorise - YouTubeYouTube
What is an SSS triangle?
When two triangles are congruent, all three pairs of corresponding sides are congruent and all three pairs of corresponding angles are congruent. If all three pairs of corresponding sides are congruent, the triangles are congruent. This congruence shortcut is known as side-side-side (SSS).
How do you prove SSS similarity theorem?
SSS Similarity Theorem: If all three pairs of corresponding sides of two triangles are proportional, then the two triangles are similar. If ABYZ=BCZX=ACXY, then ΔABC∼ΔYZX.
What is the 30-60-90 Triangle rule?
In a 30°−60°−90° triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is √3 times the length of the shorter leg. To see why this is so, note that by the Converse of the Pythagorean Theorem, these values make the triangle a right triangle.