{"id":9105,"date":"2021-12-28T21:34:32","date_gmt":"2021-12-28T16:04:32","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9105"},"modified":"2021-12-28T21:48:30","modified_gmt":"2021-12-28T16:18:30","slug":"what-is-the-value-of-tan-60-degrees","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-the-value-of-tan-60-degrees\/","title":{"rendered":"What is the Value of Tan 60 Degrees ?"},"content":{"rendered":"

Solution :<\/h2>\n

The value of tan 60 degrees<\/strong> is \\(\\sqrt{3}\\)<\/strong>.<\/p>\n

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

Consider an equilateral triangle ABC with each side of length of 2a. Each angle of \\(\\Delta\\) ABC is of 60 degrees. Let AD be the perpendicular from A on BC.<\/p>\n

\\(\\therefore\\)   AD is the bisector of \\(\\angle\\) A and D is the mid-point of BC.\"equilateral<\/p>\n

\\(\\therefore\\)   BD = DC = a and \\(\\angle\\) BAD = 30 degrees.<\/p>\n

In \\(\\Delta\\) ADB, \\(\\angle\\) D is a right angle, AB = 2a and BD = a<\/p>\n

By Pythagoras theorem,<\/p>\n

\\(AB^2\\) = \\(AD^2\\) + \\(BD^2\\)  \\(\\implies\\)  \\(2a^2\\) = \\(AD^2\\) + \\(a^2\\)<\/p>\n

\\(\\implies\\)  \\(AD^2\\) = \\(4a^2\\) – \\(a^2\\) = \\(3a^2\\)   \\(\\implies\\)  AD = \\(\\sqrt{3}a\\)<\/p>\n

Now, In triangle ADB, \\(\\angle\\) B = 60 degrees<\/p>\n

By using trigonometric formulas<\/a>,<\/p>\n

\\(tan 60^{\\circ}\\) = \\(perpendicular\\over base\\) = \\(p\\over b\\)<\/p>\n

\\(tan 60^{\\circ}\\) = side opposite to 60 degrees\/side adjacent to 60 degrees = \\(AD\\over BD\\) = \\(\\sqrt{3}a\\over a\\) = \\(\\sqrt{3}\\)<\/p>\n

Hence, the value of \\(tan 60^{\\circ}\\) = \\(\\sqrt{3}\\)<\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : The value of tan 60 degrees is \\(\\sqrt{3}\\). Proof : Consider an equilateral triangle ABC with each side of length of 2a. Each angle of \\(\\Delta\\) ABC is of 60 degrees. Let AD be the perpendicular from A on BC. \\(\\therefore\\)   AD is the bisector of \\(\\angle\\) A and D is the mid-point …<\/p>\n

What is the Value of Tan 60 Degrees ?<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[43,60],"tags":[],"yoast_head":"\nWhat is the Value of Tan 60 Degrees ? - Mathemerize<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/what-is-the-value-of-tan-60-degrees\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What is the Value of Tan 60 Degrees ? - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : The value of tan 60 degrees is (sqrt{3}). 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