Question

High school geometry anyone?

Answer 1

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.

$\frac{AB}{DB} =\frac{BC}{BE} =\frac{AC}{DE}\ \textrm{corresponding sides of similar triangles are in proportion}$  

On substituting the given values we get

$\frac{BC}{BE} =\frac{AC}{DE}$

$\frac{12}{BE} =\frac{6.75}{3}\\\\BE=5.33$

Now as B - E - C,

$BC=BE+EC$..........Addition property

substituting the given values we get

$12=5.33+EC\\\\EC=12-5.33=6.67\ ft$

Therefore the length of EC is 6.67 ft.