Answer
$b \approx 5$ cm
Work Step by Step
RECALL:
In a right triangle,
$\sin{A} = \dfrac{\text{length of opposite side}}{\text{length of hypotenuse}}
\\\cos{A} = \dfrac{\text{length of adjacent side}}{\text{length of hypotenuse}}
\\\tan{A} = \dfrac{\text{length of opposite side}}{\text{length of adjacent side}}$
Use the cosine formula to obtain:
$\cos{A} = \dfrac{\text{length of adjacent side}}{\text{length of hypotenuse}}
\\\cos{72^o}=\dfrac{b}{15}$
Multiply 15 to both sides of the equation to obtain:
$\cos{72^o} \cdot 15 = b
\\4.635254916= b
\\5 \approx b$
Thus, $b \approx 5$ cm.
