Answer:
57.5°
Step-by-step explanation:
Δ ADE and Δ ABC are similar, thus the ratios of corresponding sides are equal, that is
[tex]\frac{DE}{BC}[/tex] = [tex]\frac{AE}{AC}[/tex], that is
[tex]\frac{15}{4}[/tex] = [tex]\frac{7+AC}{AC}[/tex] ( cross- multiply )
15AC = 4(7 + AC)
15AC = 28 + 4AC ( subtract 4AC from both sides )
11AC = 28 ( divide both sides by 11 )
AC = [tex]\frac{28}{11}[/tex]
Using the tangent ratio in right [tex]\frac{opposite}{adjacent}[/tex]Δ ABC to find ∠A
cosA = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{4}{\frac{28}{11} }[/tex] = [tex]\frac{44}{28}[/tex], thus
∠A = [tex]tan^{-1}[/tex]([tex]\frac{44}{28}[/tex]) ≈ 57.5° ( to 1 dec. place )
