In-a-ABC-if-a-2-b-60-and-c-75-then-b-

Question Number 20925 by dk3029943@gmail.com last updated on 08/Sep/17

In a △ A B C, if a = 2, b = 60 ° and c = 75 °,

then b =

Answered by Joel577 last updated on 08/Sep/17

∠ A = 180 ° - (60 ° + 75 °) = 45 °

\frac{a}{\sin A} = \frac{b}{\sin B}

\frac{2}{\sin 45 °} = \frac{b}{\sin 60 °}

b = \frac{2 . \frac{\sqrt{3}}{2}}{\frac{\sqrt{2}}{2}} = \frac{2 \sqrt{3}}{\sqrt{2}} . \frac{\sqrt{2}}{\sqrt{2}} = \sqrt{6}

Answered by $@ty@m last updated on 08/Sep/17

B = 60^{o}, C = 75^{o} \Rightarrow A = 45^{o}

A p p l y i n g s i n e f o r m u l a,

\frac{a}{s i n A} = \frac{b}{s i n B}

\Rightarrow \frac{2}{s i n 45^{o}} = \frac{b}{s i n 60^{o}}

\Rightarrow \frac{2}{\frac{1}{\sqrt{2}}} = \frac{b}{\frac{\sqrt{3}}{2}}

\Rightarrow b = \sqrt{6} A n s .

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