Question

Which equation can be used to solve for b? Triangle A B C is shown. Angle B C A is a right angle and angle C A B is 30 degrees. The length of side B C is 5 centimeters, the length of B A is 10 centimeters, and the length of C A is b. tan(30o) = StartFraction 5 Over b EndFraction tan(30o) = StartFraction b Over 5 EndFraction tan(30o) = StartFraction 10 Over b EndFraction tan(30o) =

Answer 1

Answer: We should use the correct formula for tan α  (which is opposite

leg over adjacent leg)   tan α = 5/b

Step-by-step explanation:

See attached file

We must use the for equation of tan α = BC/AC  

tan α = BC/ b              tan α = 5/b      tan 30⁰  = 1/√3

b = 5/√3    ⇒ b = 5/1.7320

b = 2.8868  cm

Answer 2

Answer:

$tan30^{\circ}=\frac{5}{b}$

Step-by-step explanation:

We are given that a triangle ABC in which angle CAB=90 degrees

Angle CAB=30 degrees

Length of BC= 5 cm

Length of AB=10 cm

Length of AC=b

We have to find the equation which is used to solve  for b.

We know that

$tan\theta=\frac{Perpendicular\;side}{Base}$

Substitute the values

$tan30^{\circ}=\frac{BC}{CA}$

$tan30^{\circ}=\frac{5}{b}$

$\frac{1}{\sqrt3}=\frac{5}{b}$   ($tan30^{\circ}=\frac{1}{\sqrt3}$)

$b=5\sqrt3$

Hence, the equation can be used to solve for b is given

$tan30^{\circ}=\frac{5}{b}$