A triangle $A B C$ is to be drawn with $A B = 10 \mathrm {~cm} , B C = 7 \mathrm {~cm}$ and the angle at $A$ equal to $\theta$, where $\theta$ is a certain specified angle. Of the two possible triangles that could be drawn, the larger triangle has three times the area of the smaller one. What is the value of $\cos \theta$ ? A $\frac { 5 } { 7 }$ B $\frac { 151 } { 200 }$ C $\frac { 2 \sqrt { 2 } } { 5 }$ D $\frac { \sqrt { 17 } } { 5 }$ E $\quad \frac { \sqrt { 51 } } { 8 }$ F $\frac { \sqrt { 34 } } { 8 }$
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A triangle $A B C$ is to be drawn with $A B = 10 \mathrm {~cm} , B C = 7 \mathrm {~cm}$ and the angle at $A$ equal to $\theta$, where $\theta$ is a certain specified angle.
Of the two possible triangles that could be drawn, the larger triangle has three times the area of the smaller one.
What is the value of $\cos \theta$ ?
A $\frac { 5 } { 7 }$
B $\frac { 151 } { 200 }$
C $\frac { 2 \sqrt { 2 } } { 5 }$
D $\frac { \sqrt { 17 } } { 5 }$
E $\quad \frac { \sqrt { 51 } } { 8 }$
F $\frac { \sqrt { 34 } } { 8 }$