{"id":193880,"date":"2025-02-21T05:50:13","date_gmt":"2025-02-21T05:50:13","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=193880"},"modified":"2025-02-21T05:50:16","modified_gmt":"2025-02-21T05:50:16","slug":"find-x-round-your-answer-to-the-nearest-tenth-of-a-degree-2","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-2\/","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-1156.png\" alt=\"\" class=\"wp-image-193881\"\/><\/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 triangle provided, 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 that for any triangle with sides ( a ), ( b ), and ( c ) and angles ( A ), ( B ), and ( C ) opposite those sides, respectively, the following relationship holds:<\/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 diagram, we have the following information:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( A = 40^\\circ ) (angle at the top)<\/li>\n\n\n\n<li>( b = 23 ) (side opposite ( A ))<\/li>\n\n\n\n<li>( c = 25 ) (the hypotenuse of the triangle)<\/li>\n\n\n\n<li>( B = x ) (angle opposite side ( b ))<\/li>\n<\/ul>\n\n\n\n<p>We are trying to find angle ( B ) (or ( x )). Using the Law of Sines:<\/p>\n\n\n\n<p>[<br>\\frac{23}{\\sin 40^\\circ} = \\frac{25}{\\sin x}<br>]<\/p>\n\n\n\n<p>We can solve for ( \\sin x ) as follows:<\/p>\n\n\n\n<p>[<br>\\sin x = \\frac{25 \\cdot \\sin 40^\\circ}{23}<br>]<\/p>\n\n\n\n<p>First, let&#8217;s calculate ( \\sin 40^\\circ ) and then solve for ( x ).<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>import math\n\n# Constants\nsin_40 = math.sin(math.radians(40))\nratio = 25 * sin_40 \/ 23\n\n# Solve for x\nx_degrees = math.degrees(math.asin(ratio))\nx_degrees<\/code><\/pre>\n\n\n\n<p>After obtaining the value of ( x ), I&#8217;ll provide a detailed explanation of the calculation.<\/p>\n\n\n\n<p>The angle ( x ) is approximately ( 44.3^\\circ ).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>To find ( x ), we used the Law of Sines which states that the ratio of a side of a triangle to the sine of its opposite angle is the same for all three sides and their corresponding angles. Here&#8217;s the step-by-step breakdown of the calculation:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Using the Law of Sines<\/strong>: We know from the triangle that:<br>[<br>\\frac{23}{\\sin 40^\\circ} = \\frac{25}{\\sin x}<br>]<br>This sets up our equation based on the known angle and its opposite side, and the unknown angle ( x ) and its opposite side.<\/li>\n\n\n\n<li><strong>Rearranging the Equation<\/strong>: To isolate ( \\sin x ), we rearrange the formula:<br>[<br>\\sin x = \\frac{25 \\cdot \\sin 40^\\circ}{23}<br>]<\/li>\n\n\n\n<li><strong>Calculating ( \\sin 40^\\circ )<\/strong>: We first calculate ( \\sin 40^\\circ ) using a calculator or Python. The sine of an angle in a right triangle represents the ratio of the length of the opposite side to the hypotenuse.<\/li>\n\n\n\n<li><strong>Substituting Values<\/strong>: Plugging the value of ( \\sin 40^\\circ ) into our equation gives us the sine of angle ( x ).<\/li>\n\n\n\n<li><strong>Finding ( x )<\/strong>: Finally, using the arcsine function (inverse of sine), we calculate ( x ) from ( \\sin x ). This function returns the angle whose sine is the given number, providing us the measure of angle ( x ) in degrees.<\/li>\n<\/ol>\n\n\n\n<p>This process allows us to accurately determine the unknown angle in a non-right triangle when we have one angle and two sides. By applying these trigonometric principles, we can solve a wide range of problems involving triangles in various fields such as engineering, physics, and navigation.<\/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 triangle provided, 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 that [&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-193880","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/193880","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=193880"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/193880\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=193880"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=193880"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=193880"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}