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Amanda [17]
2 years ago
9

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) =

Mathematics
2 answers:
FinnZ [79.3K]2 years ago
4 0

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

tensa zangetsu [6.8K]2 years ago
4 0

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}

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