(a)
AB² + BC² = 33² + 56² = 4225

AC² = 65² = 4225

since AC² = AB² + BC² ,
this means triangle ABC is a rt angle triangle,
where angle ABC is 90°


(b)
cos angle ACD
= cos (180° - angle ACB)
= -cos angle ACB
= -(56/65) [ cos angle ACB = 56/65 ]
= -56/65


...

Points that should be mentioned in your answer for a)


① The triangle satisfies Pythagoras' Theorem since AB² + BC² = AC².

② △ ABC is therefore a right-angled triangle. From the equality, AC is the hypotenuse as it's the longest side of the triangle.

③ The angle opposite the hypotenuse is a right angle, 90°. Since angle ABC is opposite the hypotenuse, angle ABC = 90°