In terms of the trigonometric ratios for ΔABD, what is the length of line segment BD?

In terms of the trigonometric ratios for ΔABD, what is the length of line segment BD?

Step-by-step explanation:

∆ABD is a right triangle.

Recall: trigonometric ratios of any right triangle can easily be understood or remembered with the acronym, SOHCAHTOA.

SOH => sin(θ) = opposite/hypotenuse

CAH => Cos(θ) = adjacent/hypotenuse

TOA = tan(θ) = opposite/adjacent

Thus, the length of segment BD, in terms of trigonometric ratios for ∆ABD can be done as follows:

Let BD = x

AB = c

AD = b

=>The sine ratio for the length of line segment BD = x, using SOH.

θ = A

Opposite = DB = x

hypotenuse = AB = c

Make x the subject of formula.

=>The Cosine ratio for the length of line segment BD = x, using CAH

θ = B

Adjacent = DB = x

hypotenuse = AB = c

Make x the subject of formula.

=>The Tangent ratio for the length of line segment BD = x, using TOA

θ = A

Adjacent = DB = x

hypotenuse = AD = b

Make x the subject of formula.