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Triangle geometry

Inverses of Trigonometric Ratios

Subject: 
Algebra
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Geometry
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Euclidean geometry
Triangle geometry
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Euclidean plane geometry
Triangle
Trigonometric functions
Special right triangles
Right triangle
Ratio
Inverses of Trigonometric Ratios You've learned how to use trig ratios to solve right triangles, finding the lengths of the sides of triangles. But what if you have the sides, and need to find the angles? You know that you can take side lengths and find trig ratios, and you know you can find trig ratios (in your calculator) for angles. What is missing is a way to go from the ratios back to the original angles. And that is what "inverse trig" values are all about. If you look at your calculator, you should see, right above the "SIN", "COS", "TAN" buttons, notations along the lines of "SIN–1", "COS–1", and "TAN–1", or possibly "ASIN", "ACOS", and "ATAN". These are what you'll use to find angles from ratios.

Geometry Cheat Sheet

Subject: 
Geometry
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Exterior angle theorem
Internal and external angle
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Technology

Theorems, Conjectures, & Postulates Triangle Theorems Triangle Sum Theorem- The sum of the measures of the angles in every triangle is 180? Exterior Angle Theorem- The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. Corollary to the Triangle Sum Theorem- In a right triangle, the acute angles are complementary. Base Angles Theorem ? If two sides of a triangle are congruent, then the angles opposite them are congruent. Converse of Base Angles Theorem ? If two angles of a triangle are congruent, the sides opposite them are congruent. Corollary to the Base Angle Theorem ? If a triangle is equilateral, then it?s equiangular.

Trigonometric Functions

Subject: 
Trigonometry
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Trigonometry
Elementary mathematics
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Triangle geometry
Trigonometric functions
World Wide Web
Triangle
Education
In mathematics, the trigonometric functions (also called circular functions) are functions of an angle. They are used to relate the angles of a triangle to the lengths of the sides of a triangle. Trigonometric functions are important in the study of triangles and modeling periodic phenomena, among many other applications.

Pythagorean Theorem

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Algebra
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Area
Right triangle
Hypotenuse
Triangle
Pythagorean theorem
Definition The longest side of the triangle is called the "hypotenuse", so the formal definition is: In a right angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides. So, the square of a (a²) plus the square of b (b²) is equal to the square of c (c²): a2 + b2 = c2 Sure ... ? Let's see if it really works using an example. A "3,4,5" triangle has a right angle in it, so the formula should work. Let's check if the areas are the same: 32 + 42 = 52 Calculating this becomes: 9 + 16 = 25 Yes, it works ! Why Is This Useful?

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