{"id":252648,"date":"2025-07-11T11:16:20","date_gmt":"2025-07-11T11:16:20","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=252648"},"modified":"2025-07-11T11:16:22","modified_gmt":"2025-07-11T11:16:22","slug":"how-many-times-between-2-p-m-and-5-pm-does-the-angle-between-the-hour-hand-and-the-minute-hand-become-90-degree","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/11\/how-many-times-between-2-p-m-and-5-pm-does-the-angle-between-the-hour-hand-and-the-minute-hand-become-90-degree\/","title":{"rendered":"How many times between 2 p.m. and 5 pm does the angle between the hour hand and the minute hand become 90 degree"},"content":{"rendered":"\n<p>How many times between 2 p.m. and 5 pm does the angle between the hour hand and the minute hand become 90 degree<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To calculate how many times the angle between the hour and minute hands becomes 90 degrees between 2 p.m. and 5 p.m., let&#8217;s break it down.<\/p>\n\n\n\n<p>The angle between the hour and minute hands of a clock can be calculated using the formula: Angle=\u222330H\u22125.5M\u2223\\text{Angle} = \\left| 30H &#8211; 5.5M \\right|<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>HH is the hour.<\/li>\n\n\n\n<li>MM is the minute.<\/li>\n<\/ul>\n\n\n\n<p>We are looking for times when this angle is 90 degrees. Therefore, we want to solve the equation: \u222330H\u22125.5M\u2223=90\\left| 30H &#8211; 5.5M \\right| = 90<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: At 2 p.m. (H = 2)<\/h3>\n\n\n\n<p>For 2 p.m., the equation becomes: \u222330(2)\u22125.5M\u2223=90\\left| 30(2) &#8211; 5.5M \\right| = 90 \u222360\u22125.5M\u2223=90\\left| 60 &#8211; 5.5M \\right| = 90<\/p>\n\n\n\n<p>This gives two possible solutions:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>60\u22125.5M=9060 &#8211; 5.5M = 90 leads to M=\u22125.45M = -5.45, which is not valid.<\/li>\n\n\n\n<li>60\u22125.5M=\u22129060 &#8211; 5.5M = -90 leads to M=27.27M = 27.27.<\/li>\n<\/ol>\n\n\n\n<p>So, at 2:27:16 p.m., the angle is 90 degrees.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: At 3 p.m. (H = 3)<\/h3>\n\n\n\n<p>For 3 p.m., the equation becomes: \u222330(3)\u22125.5M\u2223=90\\left| 30(3) &#8211; 5.5M \\right| = 90 \u222390\u22125.5M\u2223=90\\left| 90 &#8211; 5.5M \\right| = 90<\/p>\n\n\n\n<p>This gives two possible solutions:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>90\u22125.5M=9090 &#8211; 5.5M = 90 leads to M=0M = 0.<\/li>\n\n\n\n<li>90\u22125.5M=\u22129090 &#8211; 5.5M = -90 leads to M=32.73M = 32.73.<\/li>\n<\/ol>\n\n\n\n<p>So, at 3:00:00 p.m. and 3:32:43 p.m., the angle is 90 degrees.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: At 4 p.m. (H = 4)<\/h3>\n\n\n\n<p>For 4 p.m., the equation becomes: \u222330(4)\u22125.5M\u2223=90\\left| 30(4) &#8211; 5.5M \\right| = 90 \u2223120\u22125.5M\u2223=90\\left| 120 &#8211; 5.5M \\right| = 90<\/p>\n\n\n\n<p>This gives two possible solutions:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>120\u22125.5M=90120 &#8211; 5.5M = 90 leads to M=5.45M = 5.45.<\/li>\n\n\n\n<li>120\u22125.5M=\u221290120 &#8211; 5.5M = -90 leads to M=38.18M = 38.18.<\/li>\n<\/ol>\n\n\n\n<p>So, at 4:05:27 p.m. and 4:38:11 p.m., the angle is 90 degrees.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p>Between 2 p.m. and 5 p.m., the angle between the hour and minute hands becomes 90 degrees at 2:27:16 p.m., 3:00:00 p.m., 3:32:43 p.m., 4:05:27 p.m., and 4:38:11 p.m.<\/p>\n\n\n\n<p>Thus, it happens <strong>five times<\/strong> during this period.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>How many times between 2 p.m. and 5 pm does the angle between the hour hand and the minute hand become 90 degree The correct answer and explanation is: To calculate how many times the angle between the hour and minute hands becomes 90 degrees between 2 p.m. and 5 p.m., let&#8217;s break it down. [&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-252648","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/252648","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=252648"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/252648\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=252648"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=252648"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=252648"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}