When I look at which posts people are viewing on this blog, inevitably one of the most popular posts is the one about Right Triangle Trigonometry (SOH-CAH-TOA) and its follow-up post with more practice problems. Today, we’ll expand on that topic by looking at how you can determine the measure of an angle in a right triangle.
Consider this problem:
In the right triangle ABC below, what is the measure, to the nearest degree, of Angle A?
This book is the first of a series covering the math concepts tested on the ACT. Our first volume focuses on “Advanced Trigonometry.” You’ll find explanations of the topics, example problems and fully done-out solutions. In the second half of the book, there are a number of problems that you can work out on your own. These, too, have fully worked-out solutions so you can check your work and really understand how to apply what you’ve learned to those tough problems that appear at the end of the ACT Math section.
The topics addressed in this book include the Law of Cosines and the Law of Sines, advanced topics in right triangle trigonometry, the three reciprocal trig functions (secant, cosecant and cotangent) and properties of functions.
Students who are taking the ACT before finishing Pre-Calculus will find this volume particularly helpful. It will cover those topics you might not have gotten to in school yet. (But even if you’ve made it through Pre-Calculus, a little extra practice never hurts, right?!?)
The book is available for your Kindle for only $2.99 and can also be read on your iPad or other tablet using the Kindle Reading app. To preview the book or make a purchase, just click on the book cover above. If you need the Kindle Reading app, you can learn more here.
One of our students has been working hard on the Math section of the ACT. He’s a very good student, so he’s been focusing a lot of his attention on the last ten problems where many of the more difficult topics are tested. Every ACT Math test contains four questions that are classified as “Trigonometry.” These questions can test the trigonometric relationship in right triangles, the properties and graphs of the trigonometric functions, and trig identities and equations. These questions go beyond the basic SOH-CAH-TOA problems that we discussed in a previous post.
Right triangle trig is usually introduced to students in Geometry, but the really rigorous examination of the topic comes later on in Pre-Calculus. There we learn that angles can be measured in something called radians as well as in degrees. You can convert an angle from degrees to radians by multiplying by π/180. The equivalent degree and radian measures for a number of important angles are shown in the diagram below.