Question Bank - General Aptitude

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In the figure below BC is perpendicular to AD, CD = 8, the measure of angle D is 60° and the measure of angle A is 45°. Find the Length of AB

A.
\(8 \sqrt {6}\)
B.
\(8 \sqrt {3}\)
C.
\(8 \sqrt {2}\)
D.
8

Solution:

Concept:\(tan~? =\frac pb\), \(sin~? =\frac ph\), \(cos~? =\frac bh\)Calculation:Given:CD = 8, ?D = 60° , ?A = 45°, ?BCD = ?BCA = 90° (BC is perpendicular to AD) In ?BCDtan 60° = \(\frac {BC}{CD} =\frac {BC}{8}\)? BC = 8 × tan 60° = \(8\sqrt {3}\)In ?ABCsin 45° = \( \frac {BC}{AB}= \frac {8\sqrt {3}}{AB} \)AB = \(\frac {8\sqrt {3}}{sin~ 45^0}= \frac {8\sqrt {3}}{\frac 1{\sqrt {2}}} =8\sqrt {6}\)

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