AC =
Round your answer to the nearest hundredth.

AC ≈ 5.03

Step-by-step explanation:

We can solve the problem above using the trigonometric ratio, they are;

SOH CAH TOA

sin Ф = opposite / hypotenuse

cosФ= adjacent/ hypotenuse

tan Ф = opposite / adjacent

From the diagram above, in reference to angle B;

opposite =AC     and   adjacent =BC

Since we have opposite and adjacent, the best formula to use is

tanФ = opposite / adjacent

tan B = AC  / BC

tan 40 =  AC/ 6

Multiply both-side of the equation by 6

6× tan 40   =  AC/ 6  ×  6

At the right-hand side of the equation, 6 will cancel-out 6 leaving us with just AC

6×tan 40 = AC

5.034598  = AC

AC ≈ 5.03   to the nearest hundredths

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