\( \newcommand{\abs}[1]{\left| \, {#1} \, \right| } \) \( \newcommand{\cm}{\mathrm{cm} } \) \( \newcommand{\sec}{ \, \mathrm{sec} \, } \) \( \newcommand{\units}[1]{\,\text{#1}} \) \( \newcommand{\vhat}[1]{\,\hat{#1}} \) \( \newcommand{\vhati}{\,\hat{i}} \) \( \newcommand{\vhatj}{\,\hat{j}} \) \( \newcommand{\vhatk}{\,\hat{k}} \) \( \newcommand{\vect}[1]{\boldsymbol{\vec{#1}}} \) \( \newcommand{\norm}[1]{\|{#1}\|} \) \( \newcommand{\arccot}{ \, \mathrm{arccot} \, } \) \( \newcommand{\arcsec}{ \, \mathrm{arcsec} \, } \) \( \newcommand{\arccsc}{ \, \mathrm{arccsc} \, } \) \( \newcommand{\sech}{ \, \mathrm{sech} \, } \) \( \newcommand{\csch}{ \, \mathrm{csch} \, } \) \( \newcommand{\arcsinh}{ \, \mathrm{arcsinh} \, } \) \( \newcommand{\arccosh}{ \, \mathrm{arccosh} \, } \) \( \newcommand{\arctanh}{ \, \mathrm{arctanh} \, } \) \( \newcommand{\arccoth}{ \, \mathrm{arccoth} \, } \) \( \newcommand{\arcsech}{ \, \mathrm{arcsech} \, } \) \( \newcommand{\arccsch}{ \, \mathrm{arccsch} \, } \)

17Calculus Precalculus - Right Triangles

Single Variable Calculus
Multi-Variable Calculus

Right Triangles

Most of the time you will be working with right triangles, which are at the heart of trigonometry. Remember from geometry that right triangles are triangles with one of the interior angles measuring 90o. This is the same as saying that one of the sides is perpendicular to another. Also remember from geometry that when you add up all the interior angles of a triangle, you get 180o. So, if you know that one of the angles is 90o, that leaves 180 - 90 = 90 for the other two angles. This is an important thing to remember when working with right triangles. First determine which angle in the 90o angle, then work with the other two whose sum will also be 90. Pretty cool, eh?

Special Right Triangles

There are several special right triangles that you will see over and over. So it is important to become very familiar with them. They are 30-60-90 and 45-45-90 triangles. The numbers refer to the interior angles. Notice that both of them have one 90o angle. So we could also call them 30-60 and 45-45 right triangles. And, if you think about it, we really only need one angle when talking about right triangles. So by saying we have a 30 degree right triangle, we have enough information about the triangle to know that we have 30-60-90 triangle.

Here are some videos that will give us some feel for these triangles.

PatrickJMT - Special Right Triangles in Geometry: 45-45-90 and 30-60-90 [13min-13secs]

video by PatrickJMT

Krista King Math - 45-45-90 Triangles [10min-53secs]

video by Krista King Math

Krista King Math - 30-60-90 Triangles [10min-6secs]

video by Krista King Math

Okay, so now that you have some knowledge about right triangles, your next tutorial is about the Unit Circle.

Really UNDERSTAND Precalculus

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