Solving trigonometry’s problem that use right angle can be done by using right triangle and Pythagorean theorem. But, in other problems it does not use right triangle.
It uses any triangles. The solution is using law of sines and cosines. It will be more complex than using right triangle but it does not mean difficult.
Table of Contents
Law of Sines
Law of sines use to solve triangle’s problem if known a pair of angles – sides and another side or angle and it will be found the pair.
In another words, law of sines can be applied if a triangle has one of the pair (in a row):
- Angle – angle – side
- Angle – side – angle
- Side – side – angle
In mathematics formula, if there is a triangle, the law of sines can be written
sinα/a = sinβ/b = sinγ/c
a/sin α = b/sin β = c/sin γ
(choose one of equation form depend on the problem. Just use two of the equation based on known in the problem)
Law of Cosines
Law of cosines is also used if there is no right triangle and the problem is finding the angle or side. It is different with law of sines. Law of cosines can be used if known:
- Side – angle – side
- Side – side – side
In mathematics, if there is any triangle, then
a2 = b2 + c2 – 2.a.b.cos α
b2 = a2 + c2 – 2.a.c.cos β
c2 = a2 + b2 – 2.a.b.cos γ
(choose one of equation depend on the problem)
remember that the sum of angles in triangle is 180°. So, if there is known two angles then the third have been known too.
- There is triangle like the picture. Find the value of x.
2. There is triangle. Find the value of x.
3. There is triangle that has 6cm, 8cm, and 12cm as the sides. Determine the value of cosines of smallest angle in the triangle.