Question

What is the length of BD?

Answer 1

Answer:

$10\sqrt{3}$

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

$\displaystyle \sin 60^\circ=\frac{\text{opposite leg}}{\text{hypotenuse}}$

$\displaystyle \sin 60^\circ=\frac{BD}{20}$

Solving for BD:

$\displaystyle BD=20\sin 60^\circ$

Since

$\sin 60^\circ=\frac{\sqrt{3}}{2}$

$\displaystyle BD=20\frac{\sqrt{3}}{2}$

Simplifying:

$\boxed{\displaystyle BD=10\sqrt{3}}$