{"id":7868,"date":"2023-04-09T22:44:00","date_gmt":"2023-04-09T17:14:00","guid":{"rendered":"https:\/\/physicscatalyst.com\/article\/?p=7868"},"modified":"2023-04-02T23:49:14","modified_gmt":"2023-04-02T18:19:14","slug":"trigonometry-formula-for-triangle","status":"publish","type":"post","link":"https:\/\/physicscatalyst.com\/article\/trigonometry-formula-for-triangle\/","title":{"rendered":"Trigonometry formula for triangle"},"content":{"rendered":"\n

For any triangle , we have following formula involving trigonometric ratios.<\/p>\n\n\n\n

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

Trigonometry formula for triangle<\/h2>\n\n\n\n

Formula 1<\/strong><\/p>\n\n\n\n

$\\frac {sin A}{a} = \\frac {sin B}{c} = \\frac {sin C}{c}$<\/p>\n\n\n\n

Formula 2<\/strong><\/p>\n\n\n\n

$cos A = \\frac {b^2 + c^2 -a^2}{2bc}$<\/p>\n\n\n\n

$cos B = \\frac {a^2 + c^2 -b^2}{2ac}$<\/p>\n\n\n\n

$cos C = \\frac {a^2 + b^2 -c^2}{2ab}$<\/p>\n\n\n\n

Formula 3<\/strong><\/p>\n\n\n\n

Area of the triangle is given by <\/p>\n\n\n\n

$S= \\sqrt {s(s-a)(s-b)(s-c)} = \\frac {1}{2} bc sin A =\\frac {1}{2} ac sin B = \\frac {1}{2} ab sin C$
where $s= \\frac {a+b+c}{2}$<\/p>\n\n\n\n

Formula 4<\/strong><\/p>\n\n\n\n

The below formula is deduced from above only<\/p>\n\n\n\n

$sin A= \\frac {2}{bc} \\sqrt {s(s-a)(s-b)(s-c)} $<\/p>\n\n\n\n

$sin B= \\frac {2}{ac} \\sqrt {s(s-a)(s-b)(s-c)} $<\/p>\n\n\n\n

$sin C= \\frac {2}{ab} \\sqrt {s(s-a)(s-b)(s-c)} $<\/p>\n\n\n\n

Formula 5<\/strong><\/p>\n\n\n\n

The Radius of the circumcenter of the triangle is given by<\/p>\n\n\n\n

$R =\\frac {abc}{4S}$<\/p>\n\n\n\n

where S is the area of the triangle<\/p>\n\n\n\n

We can write this in trigonometric relation as<\/p>\n\n\n\n

$R= \\frac {a}{2 sin A} = \\frac {b}{2 sin B}= \\frac {c}{2 sin C}= \\frac {abc}{4S}$<\/p>\n\n\n\n

Formula 6<\/strong><\/p>\n\n\n\n

a=b cos C + c Cos B
b=aCos C + c Cos A
c= aCos B + b Cos A<\/p>\n\n\n\n

Formula 7<\/strong><\/p>\n\n\n\n

The Radius of the incenter of the triangle is given by<\/p>\n\n\n\n

$r= \\frac {S}{s]}$
where S is the area of the triangle
and $s = \\frac {a+b+c}{2}$<\/p>\n\n\n\n

We can write this in trigonometric relation as<\/p>\n\n\n\n

$r=(s-a) tan \\frac {A}{2} = (s-b) tan \\frac {B}{2}= (s-c) tan \\frac {C}{2}$<\/p>\n\n\n\n

$r=4R sin \\frac {A}{2} sin \\frac {B}{2} sin \\frac {C}{2}$<\/p>\n\n\n\n

Formula 8<\/strong><\/p>\n\n\n\n

$sin \\frac {A}{2} = \\sqrt { \\frac {(s-b)(s-c}{bc}}$<\/p>\n\n\n\n

$sin \\frac {B}{2} = \\sqrt { \\frac {(s-a)(s-c}{ac}}$<\/p>\n\n\n\n

$sin \\frac {C}{2} = \\sqrt { \\frac {(s-a)(s-b}{ab}}$<\/p>\n\n\n\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

For any triangle , we have following formula involving trigonometric ratios. Trigonometry formula for triangle Formula 1 $\\frac {sin A}{a} = \\frac {sin B}{c} = \\frac {sin C}{c}$ Formula 2 $cos A = \\frac {b^2 + c^2 -a^2}{2bc}$ $cos B = \\frac {a^2 + c^2 -b^2}{2ac}$ $cos C = \\frac {a^2 + b^2 -c^2}{2ab}$ Formula […]<\/p>\n","protected":false},"author":8,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_uag_custom_page_level_css":"","site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","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":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[498],"tags":[],"class_list":["post-7868","post","type-post","status-publish","format-standard","hentry","category-maths"],"yoast_head":"\nTrigonometry formula for triangle - physicscatalyst's Blog<\/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:\/\/physicscatalyst.com\/article\/trigonometry-formula-for-triangle\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Trigonometry formula for triangle - physicscatalyst's Blog\" \/>\n<meta property=\"og:description\" content=\"For any triangle , we have following formula involving trigonometric ratios. Trigonometry formula for triangle Formula 1 $frac {sin A}{a} = frac {sin B}{c} = frac {sin C}{c}$ Formula 2 $cos A = frac {b^2 + c^2 -a^2}{2bc}$ $cos B = frac {a^2 + c^2 -b^2}{2ac}$ $cos C = frac {a^2 + b^2 -c^2}{2ab}$ Formula […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/physicscatalyst.com\/article\/trigonometry-formula-for-triangle\/\" \/>\n<meta property=\"og:site_name\" content=\"physicscatalyst's Blog\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/PhysicsCatalyst\" \/>\n<meta property=\"article:author\" content=\"https:\/\/www.facebook.com\/PhysicsCatalyst\" \/>\n<meta property=\"article:published_time\" content=\"2023-04-09T17:14:00+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2023\/04\/Trigonometry-formula-for-triangle-1.png\" \/>\n<meta name=\"author\" content=\"physicscatalyst\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"physicscatalyst\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Trigonometry formula for triangle - physicscatalyst's Blog","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/physicscatalyst.com\/article\/trigonometry-formula-for-triangle\/","og_locale":"en_US","og_type":"article","og_title":"Trigonometry formula for triangle - physicscatalyst's Blog","og_description":"For any triangle , we have following formula involving trigonometric ratios. Trigonometry formula for triangle Formula 1 $frac {sin A}{a} = frac {sin B}{c} = frac {sin C}{c}$ Formula 2 $cos A = frac {b^2 + c^2 -a^2}{2bc}$ $cos B = frac {a^2 + c^2 -b^2}{2ac}$ $cos C = frac {a^2 + b^2 -c^2}{2ab}$ Formula […]","og_url":"https:\/\/physicscatalyst.com\/article\/trigonometry-formula-for-triangle\/","og_site_name":"physicscatalyst's Blog","article_publisher":"https:\/\/www.facebook.com\/PhysicsCatalyst","article_author":"https:\/\/www.facebook.com\/PhysicsCatalyst","article_published_time":"2023-04-09T17:14:00+00:00","og_image":[{"url":"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2023\/04\/Trigonometry-formula-for-triangle-1.png","type":"","width":"","height":""}],"author":"physicscatalyst","twitter_misc":{"Written by":"physicscatalyst","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/physicscatalyst.com\/article\/trigonometry-formula-for-triangle\/#article","isPartOf":{"@id":"https:\/\/physicscatalyst.com\/article\/trigonometry-formula-for-triangle\/"},"author":{"name":"physicscatalyst","@id":"https:\/\/physicscatalyst.com\/article\/#\/schema\/person\/9b302efdc9b32e459cb1e61ab7506d3f"},"headline":"Trigonometry formula for triangle","datePublished":"2023-04-09T17:14:00+00:00","mainEntityOfPage":{"@id":"https:\/\/physicscatalyst.com\/article\/trigonometry-formula-for-triangle\/"},"wordCount":273,"commentCount":0,"publisher":{"@id":"https:\/\/physicscatalyst.com\/article\/#organization"},"image":{"@id":"https:\/\/physicscatalyst.com\/article\/trigonometry-formula-for-triangle\/#primaryimage"},"thumbnailUrl":"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2023\/04\/Trigonometry-formula-for-triangle-1.png","articleSection":["Maths"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/physicscatalyst.com\/article\/trigonometry-formula-for-triangle\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/physicscatalyst.com\/article\/trigonometry-formula-for-triangle\/","url":"https:\/\/physicscatalyst.com\/article\/trigonometry-formula-for-triangle\/","name":"Trigonometry formula for triangle - 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Trigonometry formula for triangle Formula 1 $\\frac {sin A}{a} = \\frac {sin B}{c} = \\frac {sin C}{c}$ Formula 2 $cos A = \\frac {b^2 + c^2 -a^2}{2bc}$ $cos B = \\frac {a^2 + c^2 -b^2}{2ac}$ $cos C = \\frac {a^2 + b^2 -c^2}{2ab}$ Formula…","_links":{"self":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts\/7868","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/users\/8"}],"replies":[{"embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/comments?post=7868"}],"version-history":[{"count":1,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts\/7868\/revisions"}],"predecessor-version":[{"id":7871,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts\/7868\/revisions\/7871"}],"wp:attachment":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/media?parent=7868"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/categories?post=7868"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/tags?post=7868"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}