Answer:
Therefore the length of EC is 6.67 ft.
Step-by-step explanation:
Given:
BC = 12 ft
AC = 6.75 ft
DE = 3ft
DE is parallel to AC.
Angle C is 60°.
Angle A and Angle BDE are both right angles.
Triangle ABC is similar to Triangle DBE.
To Find:
EC = ?
Solution:
Δ ABC ~ Δ DBE ..................Given
If two triangles are similar then their sides are in proportion.
[tex]\frac{AB}{DB} =\frac{BC}{BE} =\frac{AC}{DE}\ \textrm{corresponding sides of similar triangles are in proportion}\\[/tex]
On substituting the given values we get
[tex]\frac{BC}{BE} =\frac{AC}{DE}[/tex]
[tex]\frac{12}{BE} =\frac{6.75}{3}\\\\BE=5.33[/tex]
Now as B - E - C,
[tex]BC=BE+EC[/tex]..........Addition property
substituting the given values we get
[tex]12=5.33+EC\\\\EC=12-5.33=6.67\ ft[/tex]
Therefore the length of EC is 6.67 ft.
