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?
Whenever I look at the statistics for this blog, one of the most popular pages is always the post on Right Triangle Trigonometry (SOH-CAH-TOA) Problems. With that in mind, it made sense to create some more of this problems for you to try (give the people what they want, right?). So grab your calculator and a pencil and let’s give these a try!
1. In the right triangle below, what is the value of tan A?
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.
Below you’ll find seven problems similar to those found on the ACT Math test. You can solve each of these using what you know about right triangle trigonometry. Some people call these SOH-CAH-TOA problems. This is a clever acronym to remember the sine, cosine and tangent ratios.
The answers appear at the bottom of this post.
(Note: If you’d like to try even more of these problems, click here when you’re done.)
1) In the triangle below, what is the value of cos A?