{"id":193877,"date":"2025-02-21T05:48:19","date_gmt":"2025-02-21T05:48:19","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=193877"},"modified":"2025-02-21T05:48:21","modified_gmt":"2025-02-21T05:48:21","slug":"find-x-round-your-answer-to-the-nearest-tenth-of-a-degree","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/21\/find-x-round-your-answer-to-the-nearest-tenth-of-a-degree\/","title":{"rendered":"Find X. Round Your Answer To The Nearest Tenth Of A Degree"},"content":{"rendered":"\n<p>Find X. Round Your Answer To The Nearest Tenth Of A Degree.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/02\/image-1155.png\" alt=\"\" class=\"wp-image-193878\"\/><\/figure>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To solve for ( x ) in the given triangle, we can use the law of sines, which relates the sides of a triangle to the sines of its angles. The law of sines states:<\/p>\n\n\n\n<p>[<br>\\frac{a}{\\sin A} = \\frac{b}{\\sin B} = \\frac{c}{\\sin C}<br>]<\/p>\n\n\n\n<p>From the image, we know the following values:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Side ( a = 27 )<\/li>\n\n\n\n<li>Side ( c = 15 )<\/li>\n\n\n\n<li>Angle ( A = 56^\\circ )<\/li>\n<\/ul>\n\n\n\n<p>We need to find angle ( C ), which is denoted as ( x ) in the diagram.<\/p>\n\n\n\n<p>Using the law of sines:<\/p>\n\n\n\n<p>[<br>\\frac{27}{\\sin 56^\\circ} = \\frac{15}{\\sin x}<br>]<\/p>\n\n\n\n<p>First, calculate ( \\sin 56^\\circ ):<\/p>\n\n\n\n<p>[<br>\\sin 56^\\circ \\approx 0.8290<br>]<\/p>\n\n\n\n<p>Plug this value into the equation:<\/p>\n\n\n\n<p>[<br>\\frac{27}{0.8290} = \\frac{15}{\\sin x}<br>]<\/p>\n\n\n\n<p>Solve for ( \\sin x ):<\/p>\n\n\n\n<p>[<br>\\sin x = \\frac{15 \\times 0.8290}{27}<br>]<\/p>\n\n\n\n<p>[<br>\\sin x \\approx 0.4611<br>]<\/p>\n\n\n\n<p>Now, find ( x ) by taking the arcsin:<\/p>\n\n\n\n<p>[<br>x = \\sin^{-1}(0.4611)<br>]<\/p>\n\n\n\n<p>Let&#8217;s calculate the value of ( x ) and then round it to the nearest tenth of a degree.<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>import math\n\n# Calculate sin x\nsin_x = (15 * 0.8290) \/ 27\n\n# Calculate x\nx = math.degrees(math.asin(sin_x))\n\n# Round x to the nearest tenth\nx_rounded = round(x, 1)\nx_rounded<\/code><\/pre>\n\n\n\n<p>The value of ( x ) is approximately ( 27.4^\\circ ).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p>We used the law of sines to find ( x ) in the given triangle. Here\u2019s a step-by-step breakdown:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Identify Known Values:<\/strong> From the triangle, we have sides ( a = 27 ), ( c = 15 ), and angle ( A = 56^\\circ ).<\/li>\n\n\n\n<li><strong>Apply the Law of Sines:<\/strong> We utilized the relationship (\\frac{a}{\\sin A} = \\frac{c}{\\sin C}), where ( C ) is the angle we need to find.<\/li>\n\n\n\n<li><strong>Calculate (\\sin A):<\/strong> Using ( \\sin 56^\\circ \\approx 0.8290 ).<\/li>\n\n\n\n<li><strong>Rearrange to Find ( \\sin C ):<\/strong> The equation becomes (\\sin C = \\frac{15 \\times 0.8290}{27}) which simplifies to (\\sin C \\approx 0.4611).<\/li>\n\n\n\n<li><strong>Solve for ( C ):<\/strong> Using the inverse sine function, we found ( C = \\sin^{-1}(0.4611) ), yielding ( C \\approx 27.4^\\circ ).<\/li>\n<\/ol>\n\n\n\n<p>This process accurately determines the angle ( x ) using trigonometric functions and the properties of the triangle given, providing a precise and useful method in the context of geometry and trigonometry.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Find X. Round Your Answer To The Nearest Tenth Of A Degree. The Correct Answer and Explanation is : To solve for ( x ) in the given triangle, we can use the law of sines, which relates the sides of a triangle to the sines of its angles. The law of sines states: [\\frac{a}{\\sin [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"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":"","ast-disable-related-posts":"","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":[25],"tags":[],"class_list":["post-193877","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/193877","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=193877"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/193877\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=193877"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=193877"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=193877"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}