Answer
$a \approx 42$
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 tangent formula above to obtain:
$\tan{23^o} = \frac{a}{100}$
Multiply 100 on both sides of the equation to obtain:
$100 \cdot \tan{23^o} = a$
Use a scientific calculator to obtain:
$100 \cdot 0.4244748162 = a
\\42.44748162 = a
\\42 \approx a$
