Right Triangle Congruence
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Right triangle
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Algebra Sin, Cos, and Tan
Subject:
A right-angled triangle is a triangle in which one of the angles is a right-angle. The hypotenuse of a right angled triangle is the longest side, which is the one opposite the right angle. The adjacent side is the side which is between the angle in question and the right angle. The opposite side is opposite the angle in question.
In any right angled triangle, for any angle:
The sine of the angle = the length of the opposite side
the length of the hypotenuse
The cosine of the angle = the length of the adjacent side
the length of the hypotenuse
The tangent of the angle = the length of the opposite side
the length of the adjacent side
So in shorthand notation:
Sin Cos and Tan
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In a right triangle where theta is given and a side is given you can solve for anything.
To solve for the hypotenuse use the phrase SOH CAH TOA.
If the angle and the opposite are given use opposite side divided by sin of the angle. and vice versa for all other sides and angles.
Soh cah toa stands for
Sin opposite over Hypotenuse
Cosin adjacent over hypotenuse
Toa opposite over adjacent
all of these are with respect to theta.
Pythagororean Theorem
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a^2+b^2=c^2
This can only be used for right triangles. Sides a and b are the legs of the triangle. Side c is the hypotenuse.
The Pythagorean Theorem
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a^2+b^2=c^2
This theorem can only be used with right triangles. A and B are the leags and C is the hypotenuse.
Pythagorean Theorem
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This formula is extremely essential especially later on. Note that this formula only applies to right triangles. The formula is
a^2+b^2=c^2
A and B being the two legs.
C being the hypotenuse of the triangle.
The hypotenuse (c) is the side opposite the largest angle in the triangle. In this case for a right triangle, the hypotenuse will always be opposite of the right angle.
Inverses of Trigonometric Ratios
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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.
Pythagorean Theorem
Subject:
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 !
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