{"id":368,"date":"2022-04-13T10:47:59","date_gmt":"2022-04-13T10:47:59","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=368"},"modified":"2024-11-28T10:23:24","modified_gmt":"2024-11-28T10:23:24","slug":"s-7-trigonometric-ratios-find-a-side-length","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/s-7-trigonometric-ratios-find-a-side-length\/","title":{"rendered":"S.7 Trigonometric ratios: find a side length"},"content":{"rendered":"\n

Trigonometric ratios: find a side length<\/strong><\/h2>\n\n\n\n

key notes :<\/strong><\/p>\n\n\n\n

The cosine (cos) of an angle in a right triangle is a ratio. It is the length of the adjacent leg (adj) divided by the length of the hypotenuse (hyp). The adjacent leg is the leg next to the specified angle and the hypotenuse is the side across from the right angle.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Learn with an example<\/strong><\/p>\n\n\n\n

\n
\n

Find UV.<\/strong><\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Write your answer in simplified, rationalised form. Do not round.<\/p>\n\n\n\n

UV =<\/p>\n<\/div><\/div>\n\n\n\n

Find cos30\u00b0.<\/strong><\/p>\n\n\n\n

To calculate cos30\u00b0, first draw the 30\u00b0-60\u00b0-90\u00b0 special right triangle.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Calculate cos30\u00b0.<\/p>\n\n\n\n

cos 30\u00b0 = adj \/ hyp Definition of cosine<\/p>\n\n\n\n

= \u221a3\/2 Plug in adj = \u221a3 and hyp=2<\/p>\n\n\n\n

So, cos30\u00b0= \u221a3\/2 .<\/p>\n\n\n\n

Find UV.<\/strong><\/p>\n\n\n\n

Use the definition of cosine (cos) to write an equation, then solve for UV.<\/p>\n\n\n\n

cos 30\u00b0 = UV \/ 18\u221a29 Given<\/p>\n\n\n\n

\u221a3\/2 = UV \/ 18\u221a29 Substitute cos30\u00b0= \u221a3\/2<\/p>\n\n\n\n

18\u221a29 . \u221a3\/2 = UV Multiply both sides by 18\u221a29<\/p>\n\n\n\n

9 \u221a87 = UV Simplify<\/p>\n\n\n\n

So, UV= 9 \u221a87 .<\/p>\n<\/div><\/div>\n\n\n\n

\n
\n

Find CD.<\/strong><\/p>\n\n\n

\n
\"\"<\/figure><\/div>\n\n\n

Write your answer in simplified, rationalised form. Do not round.<\/p>\n\n\n\n

CD =<\/p>\n<\/div><\/div>\n\n\n\n

Find cos45\u00b0.<\/strong><\/p>\n\n\n\n

To calculate cos45\u00b0, first draw the 45\u00b0-45\u00b0-90\u00b0 special right triangle.<\/p>\n\n\n

\n
\"\"<\/figure><\/div>\n\n\n

Calculate cos45\u00b0.<\/p>\n\n\n\n

cos45\u00b0 = adj \/ hyp Definition of cosine<\/p>\n\n\n\n

= 1\/\u221a2 Plug in adj=1 and hyp= \u221a2<\/p>\n\n\n\n

= 1\/\u221a2 . \u221a2\/\u221a2<\/p>\n\n\n\n

= \u221a2\/2 Multiply<\/p>\n\n\n\n

So, cos45\u00b0= \u221a2\/2 <\/p>\n\n\n\n

Find CD.<\/p>\n\n\n\n

Use the definition of cosine (cos) to write an equation, then solve for CD.<\/p>\n\n\n\n

cos45\u00b0 = CD\/28 Given<\/p>\n\n\n\n

\u221a2\/2 = CD\/28 Substitute cos45\u00b0= \u221a2\/2<\/p>\n\n\n\n

28 . 2\/2 = CD Multiply both sides by 28<\/p>\n\n\n\n

14\u221a2 = CD Simplify<\/p>\n\n\n\n

So, CD=14\u221a2 .<\/p>\n<\/div><\/div>\n\n\n\n

let’s practice!<\/strong><\/p>\n\n\n\n

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\"\"<\/a><\/figure>\n<\/div>\n\n\n\n
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\"\"<\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Trigonometric ratios: find a side length key notes : The cosine (cos) of an angle in a right triangle is a ratio. It is the length of the adjacent leg (adj) divided by the length of the hypotenuse (hyp). The adjacent leg is the leg next to the specified angle and the hypotenuse is theContinue reading “S.7 Trigonometric ratios: find a side length”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-368","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/368","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=368"}],"version-history":[{"count":17,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/368\/revisions"}],"predecessor-version":[{"id":14948,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/368\/revisions\/14948"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=368"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}