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BITSAT 2012

Exam: BITSAT
Year: 2012
Subject: Mathematics
Chapter: Properties of Triangles

BITSAT 2012 · Mathematics · Properties of Triangles

In a triangle ABC, if a=2, B=60^ ^ and C=75^ ^ , then b equals

In a triangle

\mathrm{ABC},

if

\mathrm{a}=2, \mathrm{ B}=60^{{}^{\circ}}

and

\mathrm{C}=75^{{}^{\circ}}

, then b equals

Options

A $\sqrt{3}$
B $\sqrt{6}$
C $\sqrt{9}$
D $1+\sqrt{2}$

Correct answer

B. $\sqrt{6}$

Step-by-step solution

\mathrm{A}=180^{{}^{\circ}}-60^{{}^{\circ}}-75^{{}^{\circ}}=180^{{}^{\circ}}-135^{{}^{\circ}}=45^{{}^{\circ}}

Now,

\frac{\mathrm{a}}{\sin \mathrm{A}}=\frac{\mathrm{b}}{\sin \mathrm{B}}\Rightarrow \frac{2}{\sin 45^{{}^{\circ}}}=\frac{\mathrm{b}}{\sin 60^{{}^{\circ}}} \Rightarrow \mathrm{b}=\frac{2 \cdot(\sqrt{3} / 2)}{1 / \sqrt{2}}=\sqrt{6}

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