{"id":223458,"date":"2025-06-01T17:59:05","date_gmt":"2025-06-01T17:59:05","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=223458"},"modified":"2025-06-01T17:59:07","modified_gmt":"2025-06-01T17:59:07","slug":"how-can-i-use-trigonometry-to-find-the-height-of-a-ocean-wave-give-an-example-please","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/01\/how-can-i-use-trigonometry-to-find-the-height-of-a-ocean-wave-give-an-example-please\/","title":{"rendered":"How can i use trigonometry to find the height of a ocean wave give an example please"},"content":{"rendered":"\n

How can i use trigonometry to find the height of a ocean wave give an example please<\/p>\n\n\n\n

The Correct Answer and Explanation is :<\/mark><\/strong><\/p>\n\n\n\n

You can use trigonometry<\/strong> to find the height of an ocean wave<\/strong> by observing the wave from a fixed position and measuring angles and distances, similar to how surveyors estimate heights of objects. Here’s a step-by-step example<\/strong> and a 300-word explanation:<\/p>\n\n\n\n

\n\n\n\n

Example:<\/strong><\/h3>\n\n\n\n

You’re standing on a cliff 20 meters above sea level, observing an ocean wave. Using a clinometer or a phone app, you measure the angle of depression (from your horizontal line of sight downward) to the base<\/strong> of the wave as 40\u00b0<\/strong>, and to the crest<\/strong> (top) of the wave as 25\u00b0<\/strong>.<\/p>\n\n\n\n

What is the height of the wave?<\/p>\n\n\n\n

\n\n\n\n

Solution Using Trigonometry:<\/strong><\/h3>\n\n\n\n

Let\u2019s define:<\/p>\n\n\n\n

    \n
  • Height from your eye level to the wave crest<\/strong> = hch_c<\/li>\n\n\n\n
  • Height from your eye level to the wave base<\/strong> = hbh_b<\/li>\n\n\n\n
  • Your height above sea level = 20 m<\/li>\n<\/ul>\n\n\n\n

    We can use the tangent<\/strong> function: tan\u2061(\u03b8)=oppositeadjacent\\tan(\\theta) = \\frac{\\text{opposite}}{\\text{adjacent}}<\/p>\n\n\n\n

    Assume a fixed horizontal distance dd from you to the wave (same for both angles). Then: tan\u2061(25\u2218)=20\u2212hcd\u21d220\u2212hc=d\u22c5tan\u2061(25\u2218)(1)\\tan(25^\\circ) = \\frac{20 – h_c}{d} \\quad \\Rightarrow \\quad 20 – h_c = d \\cdot \\tan(25^\\circ) \\tag{1} tan\u2061(40\u2218)=20\u2212hbd\u21d220\u2212hb=d\u22c5tan\u2061(40\u2218)(2)\\tan(40^\\circ) = \\frac{20 – h_b}{d} \\quad \\Rightarrow \\quad 20 – h_b = d \\cdot \\tan(40^\\circ) \\tag{2}<\/p>\n\n\n\n

    Subtract (1) from (2): (20\u2212hb)\u2212(20\u2212hc)=d(tan\u2061(40\u2218)\u2212tan\u2061(25\u2218))\u21d2hc\u2212hb=d(tan\u2061(40\u2218)\u2212tan\u2061(25\u2218))(20 – h_b) – (20 – h_c) = d(\\tan(40^\\circ) – \\tan(25^\\circ)) \\Rightarrow h_c – h_b = d(\\tan(40^\\circ) – \\tan(25^\\circ))<\/p>\n\n\n\n

    Using calculator: tan\u2061(40\u2218)\u22480.8391,tan\u2061(25\u2218)\u22480.4663\u21d2hwave=d(0.8391\u22120.4663)=d(0.3728)\\tan(40^\\circ) \\approx 0.8391,\\quad \\tan(25^\\circ) \\approx 0.4663 \\Rightarrow h_{\\text{wave}} = d(0.8391 – 0.4663) = d(0.3728)<\/p>\n\n\n\n

    Now suppose the horizontal distance to the wave is 50 m<\/strong>: hwave=50\u22c50.3728=18.64 metersh_{\\text{wave}} = 50 \\cdot 0.3728 = \\boxed{18.64\\ \\text{meters}}<\/p>\n\n\n\n

    \n\n\n\n

    Explanation<\/strong><\/h3>\n\n\n\n

    Trigonometry is the study of relationships between angles and sides of triangles. In the real world, it\u2019s useful for measuring inaccessible heights or distances. To find the height of an ocean wave, we can observe the wave from a known elevation, such as a cliff or ship deck, and measure the angles of depression to both the wave\u2019s crest (top) and base (bottom).<\/p>\n\n\n\n

    By constructing imaginary right triangles from your eye level to the crest and base, we can use the tangent function<\/strong>, which relates the angle of a triangle to the ratio of the opposite side (vertical height difference) to the adjacent side (horizontal distance). The tangent of the angle equals the height difference divided by the horizontal distance to the wave.<\/p>\n\n\n\n

    After measuring the angles of depression to both the top and bottom of the wave, we compute two separate height differences and subtract them to get the wave\u2019s total height. This method assumes the wave is perpendicular to the ocean surface and the observer\u2019s height is above the sea level.<\/p>\n\n\n\n

    This approach is especially helpful when it\u2019s unsafe or impractical to measure wave heights directly, such as during a storm. Scientists, surfers, and ocean engineers often use similar principles\u2014along with instruments like clinometers or lasers\u2014to estimate wave heights for safety and research purposes.<\/p>\n\n\n\n

    Thus, trigonometry provides a safe, indirect, and mathematically sound way to estimate the height of ocean waves using just angles and distance.<\/p>\n\n\n\n

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

    How can i use trigonometry to find the height of a ocean wave give an example please The Correct Answer and Explanation is : You can use trigonometry to find the height of an ocean wave by observing the wave from a fixed position and measuring angles and distances, similar to how surveyors estimate heights […]<\/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-223458","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/223458","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=223458"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/223458\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=223458"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=223458"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=223458"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}