Answer:
The altitude is 4.1
The area of triangle DEF is 32.8
Step-by-step explanation:
An altitude drawn from angle F to the opposite side of the triangle will intercept length DE.
let the altitude = h
Apply trig-ratio to determine the value of the altitude "h";
[tex]sin (55) = \frac{h}{FE} \\\\sin (55) = \frac{h}{5} \\\\h = 5 \times sin(55)\\\\h = 5(0.8192)\\\\h = 4.096[/tex]
The area of ΔDEF using the value of the altitude is calculated as;
[tex]A = \frac{1}{2} \times base \times height\\\\A = \frac{1}{2} \times 16 \times 4.096\\\\A = 32.768 \ sq.unit\\\\A \approx 32.8 \ sq.unit[/tex]
