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

$$\mathrm{In}\mathrm{a}△ABC,\mathrm{if}a=2,b=60°\mathrm{and}c=75°,$$$$\mathrm{then}b=$$

Answered by Joel577 last updated on 08/Sep/17

$$\mathrm{\angle }A=180°-(60°+75°)=45°$$$$$$$$\frac{a}{\sin A}=\frac{b}{\sin B}$$$$\frac{2}{\sin 45°}=\frac{b}{\sin 60°}$$$$b=\frac{2.\frac{\sqrt{3}}{2}}{\frac{\sqrt{2}}{2}}=\frac{2\sqrt{3}}{\sqrt{2}}.\frac{\sqrt{2}}{\sqrt{2}}=\sqrt{6}$$

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

$$B={60}^o,C={75}^o\Rightarrow A={45}^o$$$$Applyingsineformula,$$$$\frac{a}{sinA}=\frac{b}{sinB}$$$$\Rightarrow \frac{2}{sin{45}^o}=\frac{b}{sin{60}^o}$$$$\Rightarrow \frac{2}{\frac{1}{\sqrt{2}}}=\frac{b}{\frac{\sqrt{3}}{2}}$$$$\Rightarrow b=\sqrt{6}Ans.$$

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