Answer: The value of other side is 7.8 inch.
Explanation:
It is given that the isosceles triangle has angle measures 50°, 50°, and 80°. The side across from the 80° angle is 10 inches long.
Let the given length of other equal sides be x.
The side across from the 50° angle is x inches long.
Law of sine,
[tex]\frac{a}{\sin A}= \frac{b}{\sin B} =\frac{c}{\sin C}[/tex]
[tex]\frac{x}{\sin (50)}= \frac{10}{\sin (80)}[/tex]
[tex]\frac{x}{0.766} =\frac{10}{0.9848}[/tex]
[tex]x =\frac{10}{0.9848}\times (0.766)[/tex]
[tex]x =7.778229 \approx 7.8[/tex]
Therefore, the value of other side is 7.8 inch.
