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BITSAT 2014
Exam
BITSAT
Year
2014
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

BITSAT 2014 · Mathematics · Trigonometric Ratios & Identities

An arch of a bridge is semi-elliptical with major axis horizontal....

An arch of a bridge is semi-elliptical with major axis horizontal. If the length the base is 9 meter and the highest part of the bridge is 3 meter from the horizontal; the best approximation of the height of the arch. 2 meter from the centre of the base isAn arch of a bridge is semi-elliptical with major axis horizontal. If the length the base is 9 meter and the highest

Options

  1. A11/4m11 / 4 \mathrm{ m}
  2. B8/3m8 / 3 \mathrm{ m}
  3. C7/2m7 / 2 \mathrm{ m}
  4. D2m2 \mathrm{ m}

Correct answer

B. 8/3m8 / 3 \mathrm{ m}

Step-by-step solution

An arch of a bridge is semi-elliptical with major axis horizontal. If the length the base is 9 meter and the highest
The equation of the ellipse is x2(92)2+y29=1Wherecentreisassumedasoriginandbaseas\frac{x^{2}}{\left(\frac{9}{2}\right)^{2}}+\frac{y^{2}}{9}=1 Where centre is assumed as origin and base as x−axis.Put-axis. Putx=2,weget1681+\mathrmy29=1⇒y=653≈83m(we get \frac{16}{81}+\frac{\mathrmy^{2}}{9}=1 \Rightarrow \mathrm{y}=\frac{\sqrt{65}}{3} \approx \frac{8}{3} \mathrm{ m} ( approximately)
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