Answer: [tex]16.19\ cm[/tex]
Step-by-step explanation:
Based on the data given in the exercise, we can draw the isosceles trapezoid shown in the picture attached.
As you can observe in the figure, the lenght of the longer base is:
[tex]BC=AD+x+x\\\\BC=AD+2x[/tex]
In order to find the value of "x", we need to use the following Trigonometric Identity:
[tex]tan\alpha=\frac{opposite}{adjacent}[/tex]
In this case:
[tex]\alpha =63\°\\\\opposite=10\\\\adjacent=x[/tex]
Substituting values and solving for "x". we get:
[tex]tan(63\°)=\frac{10}{x}\\\\x=\frac{10}{tan(63\°)}[/tex]
Therefore, the longer base is:
[tex]BC=AD+2x\\\\BC=6+2(\frac{10}{tan(63\°)})\\\\BC=16.19\ cm[/tex]
