Answer:
∠ w ≈ 28.1°
Step-by-step explanation:
The area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
In Δ ABC
b = BC , h = AD = 4
given the area of Δ ABC = 25 cm² , then
[tex]\frac{1}{2}[/tex] BC × AD = 25
[tex]\frac{1}{2}[/tex] BC × 4 = 25
2 BC = 25 ( divide both sides by 2 )
BC = 12.5 cm
Given the ratio of BD : DC = 2 : 3
Then DC = [tex]\frac{3}{5}[/tex] × BC = [tex]\frac{3}{5}[/tex] × 12.5 = 7.5 cm
Using the tangent ratio in right triangle ADC
tan w = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AD}{DC}[/tex] = [tex]\frac{4}{7.5}[/tex] , then
∠ w = [tex]tan^{-1}[/tex] ( [tex]\frac{4}{7.5}[/tex] ) ≈ 28.1° ( to the nearest tenth )
