+105 so a triangle is 180 degress. i have a word problem and i can only seem to get as high as 176 degrees.
Problem
suppose you have a triangle where A=47(degrees), side b=7.00, and side c=3.59. Use cosine law to find side a, angle B and angle C.
my answers so far are..
a=5.25
B=99
C=30.34
=176.
any help would be greatly appricated!!!
+26367 Hi Strider,
$$\alpha = 47\ensuremath{^\circ}\quad b=7\quad c=3.59\\
\mbox{side a?} \quad \mbox{angle } \beta \mbox{ ? and angle }\gamma \mbox{ ?}$$
a:
$$\begin{array}{l}a^2=b^2+c^2-2bc*\cos{(47\ensuremath{^\circ})} \\
a^2=7^2+3.59^2-2*7*3.59*\cos{(47\ensuremath{^\circ})} \\
a^2=27.6108624233\\
\textcolor[rgb]{1,0,0}{a=5.25460392639}
\end{array}$$
$$\mathbf{\beta}:$$
$$\begin{array}{l}b^2=a^2+c^2-2ac*\cos{(\beta) } \\
\cos{(\beta)} = \dfrac{a^2+c^2-b^2}{2ac}\\
\cos{(\beta)} = -0.22532402766\\
\textcolor[rgb]{1,0,0}{\beta=103.021932880\ensuremath{^\circ}}
\end{array}$$
$$\mathbf{\gamma}:$$
$$\begin{array}{l}c^2=a^2+b^2-2ab*\cos{(\gamma) } \\
\cos{(\gamma)} = \dfrac{a^2+b^2-c^2}{2ab}\\
\cos{(\gamma)} = 0.86621674081\\
\textcolor[rgb]{1,0,0}{\gamma=29.9780671201\ensuremath{^\circ}}
\end{array}$$
$$\boxed{\alpha + \beta +\gamma =
47\ensuremath{^\circ}
+103.021932880\ensuremath{^\circ}
+29.9780671201\ensuremath{^\circ}
=180.000000000\ensuremath{^\circ}}$$
+26367 Hi Strider,
$$\alpha = 47\ensuremath{^\circ}\quad b=7\quad c=3.59\\
\mbox{side a?} \quad \mbox{angle } \beta \mbox{ ? and angle }\gamma \mbox{ ?}$$
a:
$$\begin{array}{l}a^2=b^2+c^2-2bc*\cos{(47\ensuremath{^\circ})} \\
a^2=7^2+3.59^2-2*7*3.59*\cos{(47\ensuremath{^\circ})} \\
a^2=27.6108624233\\
\textcolor[rgb]{1,0,0}{a=5.25460392639}
\end{array}$$
$$\mathbf{\beta}:$$
$$\begin{array}{l}b^2=a^2+c^2-2ac*\cos{(\beta) } \\
\cos{(\beta)} = \dfrac{a^2+c^2-b^2}{2ac}\\
\cos{(\beta)} = -0.22532402766\\
\textcolor[rgb]{1,0,0}{\beta=103.021932880\ensuremath{^\circ}}
\end{array}$$
$$\mathbf{\gamma}:$$
$$\begin{array}{l}c^2=a^2+b^2-2ab*\cos{(\gamma) } \\
\cos{(\gamma)} = \dfrac{a^2+b^2-c^2}{2ab}\\
\cos{(\gamma)} = 0.86621674081\\
\textcolor[rgb]{1,0,0}{\gamma=29.9780671201\ensuremath{^\circ}}
\end{array}$$
$$\boxed{\alpha + \beta +\gamma =
47\ensuremath{^\circ}
+103.021932880\ensuremath{^\circ}
+29.9780671201\ensuremath{^\circ}
=180.000000000\ensuremath{^\circ}}$$
