Question

In terms of trigonometry ratios for triangle ABD, what is the length of line BD insert text on the triangle to show the length of line BD.Also just to mention the line BD bisects the line AC perpendicularly this has made the triangle ABD and the triangle BCD to be right triangles

Answer 1

ANSWER

• BD = c * sin(A)

,

• BD = c * cos(B)

,

• BD = AD * tan(A)

,

• BD = AD/tan(B)

EXPLANATION

We have to use trigonometric ratios for triangle ABD, so we can ignore triangle BCD for now,

Side BD is opposite to angle A, and side AB is the hypotenuse of the triangle. If we write the sine of A,

$\sin A=\frac{opposite}{hypotenuse}=\frac{BD}{AB}$

Solving for BD, and replacing AB by its length c,

$BD=c\sin A$

Also, side BD is the adjacent side to the angle B, so we can also use the cosine of B,

$\cos B=\frac{adjacent}{hypotenuse}=\frac{BD}{AB}$

Solving for BD,

$BD=c\cos B$

Then, we could use the tangent of A,

$\tan A=\frac{opposite}{adjacent}=\frac{BD}{AD}$

Solve for BD,

$BD=AD\tan A$

Or the tangent of B,

$\tan B=\frac{opposite}{adjacent}=\frac{AD}{BD}$

Solving for BD,

$BD=\frac{AD}{\tan B}$