Question

What is the length of BD?

Answer 1

The length of BD is 10√3

What is right triangle?

A right triangle is a type of triangle that has one angle measuring exactly 90 degrees. The side opposite the right angle is called the hypotenuse, and the other two sides are called legs.

From the figure

In ∆ABD,

∠D = 90⁰(given)

Therefore, ∆ABD is a right angled triangle.

Using trigonometric ratios

SinA = opposite/ hypotenuse

where

AB is hypotenuse

BD is opposite to ∠A

Sin60 = BD/20

BD = 20sin60

BD = 20*√(3)/2

= 10√3.

Therefore, the length of BD is 10√3

Answer 2

`10√(3)`

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=(BD)/(20)`

Solving for BD:

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

Since

`\sin 60^\circ=(√(3))/(2)`

`\displaystyle BD=20(√(3))/(2)`

Simplifying:

`\boxed{\displaystyle BD=10√(3)}`