Solve {l}{text{If}a=sqrt{3},b=1/2(sqrt{6}+sqrt{2}),c=sqrt{2},text{then}angleAtext{is}}{{lll}{text{(a)}30^circ}&{text{(b)}60^circ}&{text{(c)}75^circ}}

$$\left. \begin{array} { l } { \text { If } a = \sqrt { 3 } , b = \frac { 1 } { 2 } ( \sqrt { 6 } + \sqrt { 2 } ) , c = \sqrt { 2 } , \text { then } \angle A \text { is } } \\ { \left. \begin{array} { l l l } { \text { (a) } 30 ^ { \circ } } & { \text { (b) } 60 ^ { \circ } } & { \text { (c) } 75 ^ { \circ } } \end{array} \right. } \end{array} \right.$$

Solve for a, b, c

$$a=\sqrt{3}\approx 1.732050808$$

$$b = \frac{\sqrt{2} + \sqrt{6}}{2} \approx 1.931851653$$

$$c=\sqrt{2}\approx 1.414213562$$

Solution Steps

Consider the second equation. Use the distributive property to multiply \frac{1}{2} by \sqrt{6}+\sqrt{2}.

$$b=\frac{1}{2}\sqrt{6}+\frac{1}{2}\sqrt{2}$$

The system is now solved.

$$a=\sqrt{3} b=\frac{1}{2}\sqrt{6}+\frac{1}{2}\sqrt{2} c=\sqrt{2}$$