Answer:
AC ≈ 19.2 cm
Step-by-step explanation:
Using Pythagoras' identity in Δ BCD to find BC
BC² + BD² = DC² , that is
BC² + 12.6² = 19.3²
BC² + 158.76 = 372.49 ( subtract 158.76 from both sides )
BC² = 213.73 ( take the square root of both sides )
BC = [tex]\sqrt{213.73}[/tex] ≈ 14.62
Using the tangent ratio in Δ ABD to find AB
tan20° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AB}{BD}[/tex] = [tex]\frac{AB}{12.6}[/tex] ( multiply both sides by 12.6 )
12.6 × tan20° = AB , then
AB ≈ 4.59
Then
AC = AB + BC = 14.62 + 4.59 ≈ 19.2 cm ( to 1 dec. place )
