Answer:
see explanation
Step-by-step explanation:
(a)
Using Pythagoras' identity in right triangle ABC, that is
AC² = AB² + BC² = 3² + 5² = 9 + 25 = 34 ( take the square root of both sides )
AC = [tex]\sqrt{34}[/tex] ≈ 5.83 cm
(b)
Using the tangent ratio in right triangle ACD
tanACD = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AD}{AC}[/tex] = [tex]\frac{4}{5.83}[/tex], thus
∠ACD = [tex]tan^{-1}[/tex]( [tex]\frac{4}{5.83}[/tex]) ≈ 34.5°
