Question

Find, to the nearest degree, the three angles of a triangle with given vertices _______.

a) Trigonometry
b) Euclidean geometry
c) Angles and polygons
d) Cartesian coordinates

Answer 1

To find the angles of a triangle in mathematics, one can use trigonometric ratios or the Laws of Cosines and Sines. For right-angled triangles, the Pythagorean theorem is also applicable.

Step-by-step explanation:

The question deals with finding the three angles of a triangle, which falls under the branch of Mathematics known as trigonometry. To find the angles to the nearest degree, one can use trigonometric ratios, such as sine, cosine, and tangent, which relate the angles to the lengths of sides in a right-angled triangle. Additionally, the Law of Cosines and the Law of Sines could be useful when dealing with non-right-angled triangles.

When we have a non-right triangle, the sides and angles can be related via the Law of Cosines, which states:

`\(c^2 = a^2 + b^2 - 2ab\cdot\cos(C)\)`

and the Law of Sines, which states:

`\((a)/(\sin(A)) = (b)/(\sin(B)) = (c)/(\sin(C))\)`

For a right-angled triangle, the Pythagorean theorem, which is \(a^2 + b^2 = c^2\), is applicable. After determining the lengths of the sides using these theorems, one can apply trigonometric ratios to find the angles, thus completing the triangle analysis.