a2 = b2 + c2 - 2bc cos(alpha)
b2 = a2 + c2 - 2ac cos(beta)
c2 = a2 + b2 - 2ab cos(gamma)
There are all three formulas. Do not forget to use, arc-cos, when finding angles.
There are several different formulas. The best one to use depends on what information you have about the rest of the triangle.
The "vector triangle" illustrates the "dot product" of two vectors, represented as sides of a triangle and the enclosed angle. This can be calculated using the law of cosines. (see link)
By using Pythagoras' theorem for a right angle triangle.
half x base x perpendicular heightThe height is called the perpendicular height because it is at a right-angle to the base.
90 degree
There are several different formulas. The best one to use depends on what information you have about the rest of the triangle.
We use the law of Cosines to be able to find : 1. The measure of the third side, when the measure of two sides and the included angle of a triangle ABC are known. 2. The measure of any angle, when the measure of the three sides of a triangle ABC are known.
The "vector triangle" illustrates the "dot product" of two vectors, represented as sides of a triangle and the enclosed angle. This can be calculated using the law of cosines. (see link)
Yes, absolutely
true
By using Pythagoras' theorem for a right angle triangle.
half x base x perpendicular heightThe height is called the perpendicular height because it is at a right-angle to the base.
Acute triangle - all of the angles are less than a right angle (90°).Scalene triangle - none of the sides or angles are congruent. It can be shown that if no two angles are the same, then no two sides are the same using the Law of Sines and Law of Cosines.
90 degree
The lengths of all three sides of the triangle APEX:)
a2+b2=c2, but that only works for right triangles, where c is opposite the right angle. The law of cosines, see Related Link below, will help for non right triangles, but you need to know one of the angles.
A trapezoid is a 4-sided shape, therefore the sum of the angles adds to 360 degrees. if you continue the lines until they touch you have a triangle, whose angles sum to 180 degrees. using the law of sines, the ratio of length of a side to the sine of the angle opposite of a triangle is consistent for all three sides. using the law of cosines you are able to find the angle between any two lengths of a triangle. use these two laws to find the bottom two angles which form the base of the triangle. the remaining two angles can be found by finding the angles in the triangle that sits on top of the trapezoid, and determining their compliment angle 180 - angle = compliment angle