Question

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

Answer 1

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

Answer:

$BD = c*sin(A)$

$BD = c*cos(B)$

$BD = b*tan(A)$

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

$sin(A) = \frac{x}{c}$

Make x the subject of formula.

$c*sin(A) = x$

$BD = x = c*sin(A)$

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

θ = B

Adjacent = DB = x

hypotenuse = AB = c

$cos(B) = \frac{x}{c}$

Make x the subject of formula.

$c*cos(B) = x$

$BD = x = c*cos(B)$

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

θ = A

Adjacent = DB = x

hypotenuse = AD = b

$tan(A) = \frac{x}{b}$

Make x the subject of formula.

$b*tan(A) = x$

$BD = x = b*tan(A)$