Answer:
[tex]10\sqrt{3}[/tex]
Step-by-step explanation:
Trigonometric Ratios
This problem will be solved by the use of a trigonometric ratio called sine because it relates the opposite side of a given angle with the hypotenuse of the triangle.
Selecting the angle of 60° in triangle ABD:
Sine Ratio
[tex]\displaystyle \sin 60^\circ=\frac{\text{opposite leg}}{\text{hypotenuse}}[/tex]
[tex]\displaystyle \sin 60^\circ=\frac{BD}{20}[/tex]
Solving for BD:
[tex]\displaystyle BD=20\sin 60^\circ[/tex]
Since
[tex]\sin 60^\circ=\frac{\sqrt{3}}{2}[/tex]
[tex]\displaystyle BD=20\frac{\sqrt{3}}{2}[/tex]
Simplifying:
[tex]\boxed{\displaystyle BD=10\sqrt{3}}[/tex]
