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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Heights and Distances

NTA Abhyas 2020 · Mathematics · Heights and Distances

An isosceles triangle made of wood of base 10 feet and height 8...

An isosceles triangle made of wood of base 1010 feet and height 88 feet is placed vertically with its base on the ground and vertex directly above it. If the triangle faces the sun whose altitude is 30o3{0}^{o},& then the tangent of the angle at the apex of the shadow isAn isosceles triangle made of wood of base 10 feet and height 8 feet is placed vertically with its base on the ground

Options

  1. A803\dfrac{80}{\sqrt{3}}
  2. B803167\dfrac{80\sqrt{3}}{167}
  3. C8923\dfrac{89}{2\sqrt{3}}
  4. D803217\dfrac{80\sqrt{3}}{217}

Correct answer

B. 803167\dfrac{80\sqrt{3}}{167}

Step-by-step solution

Let,& ABCisthetriangleandABC is the triangle andBCEisitsshadowontheground<br/>Heightofthetriangularshadowis its shadow on the ground<br />Height of the triangular shadow= DE = 8cot {30}^{o} = 8\sqrt{3}feet<br/><br />∴ tan \alpha = \dfrac{5}{8\sqrt{3}} \lleft(from\Delta BDE)<br/><br />⇒ tan \l(2α)=2tanα1−tan2α<br/><imgsrc="/api/proxy−image?url=https\l\left(2\alpha\right) = \dfrac{2tan \alpha}{1 - tan^{2}\alpha}<br /><img src="/api/proxy-image?url=https%3A%2F%2Ffirebasestorage.googleapis.com%2Fv0%2Fb%2Fquantrexacademy-app.firebasestorage.app%2Fo%2Fquestions%252Ffigs%252Fnta_abhyas%252Fjee_main%252Fimages%252F1fdabeb9-85b0-4245-bc30-f89763d1e137.png%3Falt%3Dmedia&clean=1&v=wm2" data-qx-orig-src="https://firebasestorage.googleapis.com/v0/b/quantrexacademy-app.firebasestorage.app/o/questions%2Ffigs%2Fnta_abhyas%2Fjee_main%2Fimages%2F1fdabeb9-85b0-4245-bc30-f89763d1e137.png?alt=media" data-qx-storage-src="https://firebasestorage.googleapis.com/v0/b/quantrexacademy-app.firebasestorage.app/o/questions%2Ffigs%2Fnta_abhyas%2Fjee_main%2Fimages%2F1fdabeb9-85b0-4245-bc30-f89763d1e137.png?alt=media" style="width:1.38681in;height:1.77361in" /><br />=\dfrac{2\dfrac{5}{8\sqrt{3}}}{1 - \dfrac{25}{192}} = \dfrac{5}{4\sqrt{3}} \times \dfrac{192}{167} = \dfrac{80\sqrt{3}}{167}
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