Answer:
∠BAC = 35°
AC = 5 cm
BD = 2.4 cm
Step-by-step explanation:
As ΔABC ~ ΔBDC then ∠CBD ≅ ∠BAC
As ∠CBD = 35° then ∠BAC = 35°
Using Pythagoras' Theorem
CB² + AB² = AC²
⇒ 3² + 4² = AC²
⇒ 25 = AC²
⇒ AC = 5 cm
As ΔABC ~ ΔBDC then
AB : AC = BD : BC
⇒ 4 : 5 = BD : 3
[tex]\sf \implies \dfrac45=\dfrac{BD}{3}[/tex]
[tex]\sf \implies BD=\dfrac{12}{5}=2.4\:cm[/tex]
**A right triangle with legs of 3cm and 4cm, and a perpendicular line from the hypotenuse to the right angle vertex, does not have an internal angle CBD of 35°. It should be 36.87°. So if you use SOHCAHTOA to find the length of BD, it will be incorrect. See attached diagram**
