Trigonometry Math Full Solution Thinking Question

Question

In Rectangle ABCD, ∠EFC = 90°, and CF bisects ∠DCE. AΔCDF : AΔFAE = 16 : 9. (Hint: similar triangles)

a) Determine tan∠FEC.

b) If CD = 8cm, Determine the area of rectangle ABCD.

Diagram:

Answer 1

I concur on tan answer of angle FEC = 4/3

as for area if cd=8

see angle FCD=90-angle FEC and angle AFE=90- angle FEC

cd=8 implies df=6, from tan(FEC)=cot(FCD)=4/3

df=6 implies cf=10 ,,,,pythagorean theorem

cf=10 implies fe=7.5 from tan(FEC)=4/3

call fa=x, then ae=(3/4)x ,,,,,,from tan(FEC)=cot(AFE)=4/3

and 7.5²=(25/16)x² ,,,,,pythagorean theorem

x=6

so length is 6+6=12 and area=8*12=96 square cm.

Answer 2

The scale factor between the two similar triangles is 4 : 3.

tan FEC = CF / EF

CF / EF = 4 / 3

tan FEC = 4 / 3