{"id":87292,"date":"2025-06-01T06:39:32","date_gmt":"2025-06-01T06:39:32","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=87292"},"modified":"2025-06-01T06:39:32","modified_gmt":"2025-06-01T06:39:32","slug":"when-the-sun-is-30-above-the-horizon-shadow-of-one-tree-is-17%c2%b73-m-lo","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/when-the-sun-is-30-above-the-horizon-shadow-of-one-tree-is-17%c2%b73-m-lo\/","title":{"rendered":"When the sun is 30\u00b0 above the horizon, shadow of one tree is 17\u00b73 m lo"},"content":{"rendered":"

When the sun is 30\u00b0 above the horizon, shadow of one tree is 17\u00b73 m long. What is the height of this tree ?<\/p>\n

[amp_mcq option1=”20 m” option2=”17\u00b730 m” option3=”10 m” option4=”1\u00b773 m” correct=”option3″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC NDA-1 – 2015<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThis problem can be solved using trigonometry, specifically the tangent function in a right-angled triangle.
\n<\/section>\n
\nThe tree stands vertically, forming a right angle with the ground. The sun’s rays create a shadow on the ground. The angle of elevation of the sun (30\u00b0) is the angle between the ground (shadow) and the line from the end of the shadow to the top of the tree. Let H be the height of the tree (opposite side) and L be the length of the shadow (adjacent side). We have the relationship: tan(angle) = Opposite \/ Adjacent. So, tan(30\u00b0) = H \/ L.
\nGiven L = 17.3 m and tan(30\u00b0) = 1\/$\\sqrt{3}$.
\nH = L * tan(30\u00b0) = 17.3 m * (1\/$\\sqrt{3}$).
\n<\/section>\n
\nThe value of $\\sqrt{3}$ is approximately 1.732.
\nH $\\approx$ 17.3 \/ 1.732.
\nNotice that 17.3 is very close to 10 * 1.73. If we assume the shadow length is precisely $10\\sqrt{3}$ meters (which is approximately 17.32 m), then:
\nH = $(10\\sqrt{3}) \\times (1\/\\sqrt{3}) = 10$ meters.
\nGiven the options, 10 m is the most likely intended answer, implying the shadow length 17.3 m was an approximation for $10\\sqrt{3}$ m.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

When the sun is 30\u00b0 above the horizon, shadow of one tree is 17\u00b73 m long. What is the height of this tree ? [amp_mcq option1=”20 m” option2=”17\u00b730 m” option3=”10 m” option4=”1\u00b773 m” correct=”option3″] This question was previously asked in UPSC NDA-1 – 2015 Download PDFAttempt Online This problem can be solved using trigonometry, specifically … <\/p>\n

Detailed SolutionWhen the sun is 30\u00b0 above the horizon, shadow of one tree is 17\u00b73 m lo<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1093],"tags":[1443,1129,1128],"class_list":["post-87292","post","type-post","status-publish","format-standard","hentry","category-upsc-nda-1","tag-1443","tag-mechanics","tag-physics","no-featured-image-padding"],"yoast_head":"\nWhen the sun is 30\u00b0 above the horizon, shadow of one tree is 17\u00b73 m lo<\/title>\n<meta name=\"description\" content=\"This problem can be solved using trigonometry, specifically the tangent function in a right-angled triangle. The tree stands vertically, forming a right angle with the ground. The sun's rays create a shadow on the ground. The angle of elevation of the sun (30\u00b0) is the angle between the ground (shadow) and the line from the end of the shadow to the top of the tree. Let H be the height of the tree (opposite side) and L be the length of the shadow (adjacent side). We have the relationship: tan(angle) = Opposite \/ Adjacent. So, tan(30\u00b0) = H \/ L. Given L = 17.3 m and tan(30\u00b0) = 1\/$sqrt{3}$. H = L * tan(30\u00b0) = 17.3 m * (1\/$sqrt{3}$).\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/when-the-sun-is-30-above-the-horizon-shadow-of-one-tree-is-17\u00b73-m-lo\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"When the sun is 30\u00b0 above the horizon, shadow of one tree is 17\u00b73 m lo\" \/>\n<meta property=\"og:description\" content=\"This problem can be solved using trigonometry, specifically the tangent function in a right-angled triangle. The tree stands vertically, forming a right angle with the ground. The sun's rays create a shadow on the ground. The angle of elevation of the sun (30\u00b0) is the angle between the ground (shadow) and the line from the end of the shadow to the top of the tree. Let H be the height of the tree (opposite side) and L be the length of the shadow (adjacent side). We have the relationship: tan(angle) = Opposite \/ Adjacent. So, tan(30\u00b0) = H \/ L. Given L = 17.3 m and tan(30\u00b0) = 1\/$sqrt{3}$. H = L * tan(30\u00b0) = 17.3 m * (1\/$sqrt{3}$).\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/when-the-sun-is-30-above-the-horizon-shadow-of-one-tree-is-17\u00b73-m-lo\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T06:39:32+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"When the sun is 30\u00b0 above the horizon, shadow of one tree is 17\u00b73 m lo","description":"This problem can be solved using trigonometry, specifically the tangent function in a right-angled triangle. The tree stands vertically, forming a right angle with the ground. The sun's rays create a shadow on the ground. The angle of elevation of the sun (30\u00b0) is the angle between the ground (shadow) and the line from the end of the shadow to the top of the tree. Let H be the height of the tree (opposite side) and L be the length of the shadow (adjacent side). We have the relationship: tan(angle) = Opposite \/ Adjacent. So, tan(30\u00b0) = H \/ L. Given L = 17.3 m and tan(30\u00b0) = 1\/$sqrt{3}$. H = L * tan(30\u00b0) = 17.3 m * (1\/$sqrt{3}$).","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/when-the-sun-is-30-above-the-horizon-shadow-of-one-tree-is-17\u00b73-m-lo\/","og_locale":"en_US","og_type":"article","og_title":"When the sun is 30\u00b0 above the horizon, shadow of one tree is 17\u00b73 m lo","og_description":"This problem can be solved using trigonometry, specifically the tangent function in a right-angled triangle. The tree stands vertically, forming a right angle with the ground. The sun's rays create a shadow on the ground. The angle of elevation of the sun (30\u00b0) is the angle between the ground (shadow) and the line from the end of the shadow to the top of the tree. Let H be the height of the tree (opposite side) and L be the length of the shadow (adjacent side). We have the relationship: tan(angle) = Opposite \/ Adjacent. So, tan(30\u00b0) = H \/ L. Given L = 17.3 m and tan(30\u00b0) = 1\/$sqrt{3}$. H = L * tan(30\u00b0) = 17.3 m * (1\/$sqrt{3}$).","og_url":"https:\/\/exam.pscnotes.com\/mcq\/when-the-sun-is-30-above-the-horizon-shadow-of-one-tree-is-17\u00b73-m-lo\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T06:39:32+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/when-the-sun-is-30-above-the-horizon-shadow-of-one-tree-is-17%c2%b73-m-lo\/","url":"https:\/\/exam.pscnotes.com\/mcq\/when-the-sun-is-30-above-the-horizon-shadow-of-one-tree-is-17%c2%b73-m-lo\/","name":"When the sun is 30\u00b0 above the horizon, shadow of one tree is 17\u00b73 m lo","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T06:39:32+00:00","dateModified":"2025-06-01T06:39:32+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"This problem can be solved using trigonometry, specifically the tangent function in a right-angled triangle. 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