Answer and Explanation: The laws of cosine are used to determine the area of a triangle and the obtained area is known as Heron's formula. We know that the area of a triangle in terms of two sides and one angle is Area = 1 2 b c sin .
It is also called the cosine rule. If ABC is a triangle, then as per the statement of cosine law, we have: a2 = b2 + c2 – 2bc cos α, where a,b, and c are the sides of triangle and α is the angle between sides b and c.
The area rule states that the area of any triangle is equal to half the product of the lengths of the two sides of the triangle multiplied by the sine of the angle included by the two sides.
The Cosine Rule can be used in any triangle where you are trying to relate all three sides to one angle. If you need to find the length of a side, you need to know the other two sides and the opposite angle.
The cosine of a right angle is 0, so the law of cosines, c2 = a2 + b2 – 2ab cos C, simplifies to becomes the Pythagorean identity, c2 = a2 + b2, for right triangles which we know is valid.
The Law of Cosines is useful for finding: the third side of a triangle when we know two sides and the angle between them (like the example above) the angles of a triangle when we know all three sides (as in the following example)
To solve a triangle is to find the lengths of each of its sides and all its angles. 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.
Area is calculated by multiplying the length of a shape by its width.
What Is a “30-60-90” Triangle? A special right triangle with angles 30°, 60°, and 90° is called a 30-60-90 triangle. The angles of a 30-60-90 triangle are in the ratio 1 : 2 : 3. Since 30° is the smallest angle in the triangle, the side opposite to the 30° angle is always the smallest (shortest leg).
Cos 90° = 0
Also, it is easy to remember the special values like 0°, 30°, 45°, 60°, and 90° since all the values are present in the first quadrant.
A convenient mnemonic for remembering the definition of the sine, cosine, and tangent is SOHCAHTOA (sine equals opposite over hypotenuse, cosine equals adjacent over hypotenuse, tangent equals opposite over adjacent).
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.
noun Trigonometry. a law stating that the square of a side of a plane triangle is equal to the sum of the squares of the other two sides minus twice the product of the other sides multiplied by the cosine of the angle between them.
Solving right triangles
We can use the Pythagorean theorem and properties of sines, cosines, and tangents to solve the triangle, that is, to find unknown parts in terms of known parts. Pythagorean theorem: a2 + b2 = c2. Sines: sin A = a/c, sin B = b/c.
Trigonometry (from Ancient Greek τρίγωνον (trígōnon) 'triangle', and μέτρον (métron) 'measure') is a branch of mathematics concerned with relationships between angles and ratios of lengths. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.
Calculus, as it is practiced today, was invented in the 17th century by British scientist Isaac Newton (1642 to 1726) and German scientist Gottfried Leibnitz (1646 to 1716), who independently developed the principles of calculus in the traditions of geometry and symbolic mathematics, respectively.
The origins of algebra precede his birth by 2,500 years — in ancient Babylonia, Egypt and Athens. The earliest known origins are the Rhind mathematical papyrus, written by the scribe Ahmes (or Ahmose) in Egypt around 1650 BC.
Muhammad ibn Musa al-Khwarizmi was a 9th-century Muslim mathematician and astronomer. He is known as the “father of algebra”, a word derived from the title of his book, Kitab al-Jabr. His pioneering work offered practical answers for land distribution, rules on inheritance and distributing salaries.
The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line. It is basically used to get the distance of the two objects where the angles and an object's distance from the ground are known to us.