That is a bit complicated. You need to know sines and cosines and more geometry.
Given area K and 2 sides a and b ,the relation is K = (1/2) (absinC); solve for angle C; then the third side c, from law of cosines is c =sqrt (a squared +b squared -2abcosC); then sin A = 2K/bc and
sin B = 2K/ac. solve for angles B and C. In your case, approximately, C = 56 degrees, A =52 degrees and B = 72 degrees
no. If it is a right angled triangle. Then using Pythagoras' formula a2 +b2 =c2
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)
If you know all three sides of a triangle, you can calculate the angles using the law of cosines. If you only want to know which angle is the smallest, it is much simpler: The angle that is opposite to the smallest side is the smallest angle; the angle that is opposite to the largest side is the largest angle.
Given two sides and the angle between them, you can use the formula: Area = 1/2*a*b*sinѲ Where a and b are the sides, and Ѳ the angle between them.
By using trigonometry or using Pythagoras' theorem for a right angle triangle.
The 3rd side of the right angle triangle can be found by using Pythagoras' theorem.
If you have the length of two of the sides and one other angle you can use the law of sines.
no. If it is a right angled triangle. Then using Pythagoras' formula a2 +b2 =c2
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.
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)
If you know all three sides of a triangle, you can calculate the angles using the law of cosines. If you only want to know which angle is the smallest, it is much simpler: The angle that is opposite to the smallest side is the smallest angle; the angle that is opposite to the largest side is the largest angle.
Given two sides and the angle between them, you can use the formula: Area = 1/2*a*b*sinѲ Where a and b are the sides, and Ѳ the angle between them.
By using the cosine rule in trigonometry the biggest angle works out as 106.23 degrees.
By using trigonometry or using Pythagoras' theorem for a right angle triangle.
The angle directly opposite the hypotenuse is always 90o in a right angle triangle and if you know the other sides you can work out the other angles using one of the three trigonometry equations. Sin, Tan or Cos then use the inverse and you will get the degree.
The largest angle of the triangle will be opposite its largest side and by using the Cosine Rule it works out as 106.23 degrees.
Using the cosine rule: 13.0112367 cm The triangle is in fact an isosceles triangle.