{"id":1402,"date":"2013-02-22T05:40:23","date_gmt":"2013-02-22T05:40:23","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=1402"},"modified":"2018-07-03T22:33:44","modified_gmt":"2018-07-03T22:33:44","slug":"math-trigonometry-the-tangent-ratio","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/math-trigonometry-the-tangent-ratio\/","title":{"rendered":"Math: Trigonometry: The Tangent Ratio"},"content":{"rendered":"

As a math tutor, you explain the tangent ratio a few times a year.<\/h1>\n

Trigonometry involves finding unknown sides and angles of triangles. \u00a0At first, it only involves “right” triangles – that is, ones that contain a 90\u00ba angle.<\/p>\n

At beginner’s level, there are three trigonometric functions: sin, cos, and tan.\u00a0(Of course, tan is short for tangent.) \u00a0Note their presence on any scientific calculator. \u00a0By the way: \u00a0in most cases, if a calculator has sin, cos, and tan keys, it’s probably got all you need for high school.<\/p>\n

Understanding sin, cos, and tan means understanding how the sides of a triangle are named.<\/p>\n

The hypotenuse is always the longest side.<\/p>\n

The remaining two sides are called the legs. \u00a0The leg touching the angle of interest is called the adjacent side; the other leg is the opposite.<\/p>\n

Note that the following diagram, like most diagrams in trig, is not to scale.<\/strong>
\n\"\"<\/p>\n

The capital letters refer to angles A, B, and C. \u00a0If A is the angle of interest, then the adjacent side is 11, and the opposite is 13. \u00a0If, on the other hand, B is the angle of interest, then the adjacent side is 13, while the opposite is 11.<\/p>\n

The definition of tan is as follows:<\/p>\n

tan=opposite\/adjacent<\/p>\n

Therefore, in the diagram above,<\/p>\n

tanA=13\/11<\/p>\n

Here’s where we get practical: \u00a0if you know the angle of interest, then your calculator knows its tan ratio. \u00a0For instance, tan32\u00ba=0.625, rounded to three decimal places. \u00a0(Make sure your calculator is set to degrees.)<\/p>\n

Let’s use the tangent ratio (known affectionately as tan) to solve a height question:<\/p>\n

Problem:<\/strong><\/p>\n

When the sun is at 40\u00ba elevation, a tree casts a shadow 13m long. \u00a0How high is the tree?<\/p>\n

Solution:<\/strong><\/p>\n

First, we draw a diagram:<\/p>\n

\"\"<\/p>\n

Note that the box in the corner means 90\u00ba.<\/p>\n

Looking at the diagram, we see that relative to the 40\u00ba angle,\u00a0the height, h, is the opposite side. \u00a013m is the adjacent side. \u00a0Remembering that<\/p>\n

tan=opposite\/adjacent<\/p>\n

it follows that, in our case,<\/p>\n

\"\"<\/p>\n

Of course,<\/p>\n

\"\"<\/p>\n

So then<\/p>\n

\"\"<\/p>\n

Using the method of cross-multiplication described previously in\u00a0this post<\/a>, we proceed:<\/p>\n

\"\"<\/p>\n

so that we have<\/p>\n

h(1)=13(tan40\u00ba)<\/strong><\/p>\n

h=10.9m<\/strong><\/p>\n

Apparently the tree is 10.9m high.<\/p>\n

Hope this gets you on the way to calculating those heights that seemed out of reach until now:)<\/p>\n

Jack of Oracle Tutoring by Jack and Diane,<\/a>\u00a0Campbell River, BC.<\/p>\n","protected":false},"excerpt":{"rendered":"

As a math tutor, you explain the tangent ratio a few times a year. Trigonometry involves finding unknown sides and angles of triangles. \u00a0At first, it only involves “right” triangles – that is, ones that contain a 90\u00ba angle. At …<\/p>\n

Math: Trigonometry: The Tangent Ratio<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[2744,2745],"class_list":["post-1402","post","type-post","status-publish","format-standard","hentry","category-math","tag-how-to-use-tan","tag-the-tangent-ratio-to-find-a-height"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/1402","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/comments?post=1402"}],"version-history":[{"count":43,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/1402\/revisions"}],"predecessor-version":[{"id":35293,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/1402\/revisions\/35293"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=1402"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=1402"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=1402"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}