Answer:
∠ ABC = 75°
Step-by-step explanation:
using the sine ratio in right Δ ABD
sin ABD = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AD}{AB}[/tex] = [tex]\frac{4}{8}[/tex] = [tex]\frac{1}{2}[/tex] , then
∠ ABD = [tex]sin^{-1}[/tex] ( [tex]\frac{1}{2}[/tex] ) = 30°
Using the sine ratio in right Δ CBD
sin CBD = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{CD}{BC}[/tex] = [tex]\frac{3}{3\sqrt{2} }[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] , then
∠ CBD = [tex]sin^{-1}[/tex] ( [tex]\frac{1}{\sqrt{2} }[/tex] ) = 45°
Then
∠ ABC = ∠ABD + ∠ CBD = 30° + 45° = 75°
