{"id":228974,"date":"2025-06-07T19:07:06","date_gmt":"2025-06-07T19:07:06","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=228974"},"modified":"2025-06-07T19:07:08","modified_gmt":"2025-06-07T19:07:08","slug":"what-is-the-value-of-d-to-the-nearest-hundredth-d-7-2-d-42-d","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/07\/what-is-the-value-of-d-to-the-nearest-hundredth-d-7-2-d-42-d\/","title":{"rendered":"What is the value of d to the nearest hundredth? d 7.2 D 42\u00b0 d"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">What is the value of d to the nearest hundredth? d 7.2 D 42\u00b0 d<br>E What is the value of d to the nearest hundredth? d 7.2 D 42\u00b0 d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To find the value of <strong>d<\/strong> to the nearest hundredth, we are likely dealing with a triangle where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>One side is <strong>7.2 units<\/strong>,<\/li>\n\n\n\n<li>One angle is <strong>42\u00b0<\/strong>, and<\/li>\n\n\n\n<li>We are solving for side <strong>d<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Assuming this is a <strong>non-right triangle<\/strong> and angle <strong>D = 42\u00b0<\/strong>, and we are given side <strong>opposite angle D as 7.2<\/strong>, and we are solving for another side <strong>d<\/strong>, we need more context\u2014either:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Another angle and its opposite side (to use the <strong>Law of Sines<\/strong>), or<\/li>\n\n\n\n<li>Two sides and the included angle (to use the <strong>Law of Cosines<\/strong>).<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Let\u2019s assume the problem intends us to use the <strong>Law of Sines<\/strong>, meaning: dsin\u2061(D)=7.2sin\u2061(other&nbsp;angle)\\frac{d}{\\sin(D)} = \\frac{7.2}{\\sin(\\text{other angle})}sin(D)d\u200b=sin(other&nbsp;angle)7.2\u200b<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">But since we don\u2019t have any other angle or triangle configuration explicitly given, the only reasonable interpretation is that <strong>d is opposite the 42\u00b0 angle<\/strong>, and the side of length <strong>7.2<\/strong> is adjacent to it, forming a right triangle.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Interpretation: Right Triangle with:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>angle D = 42\u00b0<\/li>\n\n\n\n<li>adjacent side to D = 7.2<\/li>\n\n\n\n<li>hypotenuse = d<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Then, we can use the <strong>cosine function<\/strong>: cos\u2061(42\u2218)=7.2d\\cos(42^\\circ) = \\frac{7.2}{d}cos(42\u2218)=d7.2\u200b<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Solving for <strong>d<\/strong>: d=7.2cos\u2061(42\u2218)\u22487.20.7431\u22489.69d = \\frac{7.2}{\\cos(42^\\circ)} \\approx \\frac{7.2}{0.7431} \\approx 9.69d=cos(42\u2218)7.2\u200b\u22480.74317.2\u200b\u22489.69<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 Final Answer:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">9.69\\boxed{9.69}9.69\u200b<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation <\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">In trigonometry, we often encounter problems involving triangles where we need to solve for unknown sides or angles using functions like sine, cosine, or tangent. In this case, we are given a side of a triangle measuring 7.2 units and an angle of 42\u00b0, and we are asked to find the side <strong>d<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The key step is identifying the correct trigonometric relationship. Since we\u2019re told the 7.2-unit side is adjacent to the 42\u00b0 angle and we are solving for the hypotenuse <strong>d<\/strong>, this forms a right triangle scenario. In right triangles, the <strong>cosine<\/strong> of an angle equals the length of the adjacent side divided by the hypotenuse: cos\u2061(\u03b8)=adjacenthypotenuse\\cos(\\theta) = \\frac{\\text{adjacent}}{\\text{hypotenuse}}cos(\u03b8)=hypotenuseadjacent\u200b<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Substituting our values: cos\u2061(42\u2218)=7.2d\\cos(42^\\circ) = \\frac{7.2}{d}cos(42\u2218)=d7.2\u200b<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To isolate <strong>d<\/strong>, we multiply both sides of the equation by <strong>d<\/strong>, then divide by <strong>cos(42\u00b0)<\/strong>: d=7.2cos\u2061(42\u2218)\u22487.20.7431\u22489.69d = \\frac{7.2}{\\cos(42^\\circ)} \\approx \\frac{7.2}{0.7431} \\approx 9.69d=cos(42\u2218)7.2\u200b\u22480.74317.2\u200b\u22489.69<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Using a calculator or trigonometric table, we find <strong>cos(42\u00b0) \u2248 0.7431<\/strong>. This leads us to the final result: <strong>d \u2248 9.69<\/strong> units, rounded to the nearest hundredth.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This problem demonstrates how trigonometric ratios allow us to find unknown sides in right triangles when at least one angle and one side are known. It&#8217;s a fundamental technique in geometry, physics, and real-world applications such as engineering and navigation.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner4-667.jpeg\" alt=\"\" class=\"wp-image-228975\"\/><\/figure>\n\n\n","protected":false},"excerpt":{"rendered":"<p>What is the value of d to the nearest hundredth? d 7.2 D 42\u00b0 dE What is the value of d to the nearest hundredth? d 7.2 D 42\u00b0 d The Correct Answer and Explanation is: To find the value of d to the nearest hundredth, we are likely dealing with a triangle where: Assuming [&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-228974","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/228974","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=228974"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/228974\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=228974"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=228974"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=228974"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}