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a=192 b=291 C=41.3 find missing sides and angles

 May 7, 2014

Best Answer 

 #1
avatar+33665 
+5

I take it C is the angle, and you are talking about a triangle in which case you can use the Cosine rule in the form

$$c^2=a^2+b^2-2abcos(C)$$  to find c.

$${\mathtt{c}} = {\sqrt{{{\mathtt{192}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{291}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{192}}{\mathtt{\,\times\,}}{\mathtt{291}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\mathtt{41.3}}^\circ\right)}}} \Rightarrow {\mathtt{c}} = {\mathtt{193.896\: \!211\: \!065\: \!943\: \!792\: \!5}}$$

or c ≈193.9

I'll leave you to use the sine rule $$\frac{sin(A)}{a}=\frac{sin(C)}{c}$$ to find A, and similarly for B (or just use the fact that the three angles must add to 90° to get the last one). 

 May 8, 2014
 #1
avatar+33665 
+5
Best Answer

I take it C is the angle, and you are talking about a triangle in which case you can use the Cosine rule in the form

$$c^2=a^2+b^2-2abcos(C)$$  to find c.

$${\mathtt{c}} = {\sqrt{{{\mathtt{192}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{291}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{192}}{\mathtt{\,\times\,}}{\mathtt{291}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\mathtt{41.3}}^\circ\right)}}} \Rightarrow {\mathtt{c}} = {\mathtt{193.896\: \!211\: \!065\: \!943\: \!792\: \!5}}$$

or c ≈193.9

I'll leave you to use the sine rule $$\frac{sin(A)}{a}=\frac{sin(C)}{c}$$ to find A, and similarly for B (or just use the fact that the three angles must add to 90° to get the last one). 

Alan May 8, 2014

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