Answer:
[tex]\angle D=37.7^{\circ}[/tex]
[tex]\angle E=52.3^{\circ}[/tex]
[tex]FD\approx 28.5[/tex]
Step-by-step explanation:
Please find the attachment.
We have been given that angle FED with angle F=90 degree, ED=36, and FE=22. We are asked to find the unknown angles and the unknown side length of the triangle.
We will use sine to solve for angle D as:
[tex]\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]
[tex]\text{sin}(D)=\frac{22}{36}[/tex]
[tex]D=\text{sin}^{-1}(\frac{22}{36})[/tex]
[tex]D=37.66988696^{\circ}[/tex]
[tex]D\approx 37.7^{\circ}[/tex]
Therefore, measure of angle D is 37.7 degrees.
Now, we will find measure of angle E using angle sum property.
[tex]m\angle E+m\angle F+m\angle D=180^{\circ}[/tex]
[tex]m\angle E+90^{\circ}+37.7^{\circ}=180^{\circ}[/tex]
[tex]m\angle E+127.7^{\circ}=180^{\circ}[/tex]
[tex]m\angle E+127.7^{\circ}-127.7^{\circ}=180^{\circ}-127.7^{\circ}[/tex]
[tex]m\angle E=52.3^{\circ}[/tex]
Therefore, measure of angle E is 52.3 degrees.
We will use Pythagoras theorem to solve for side FD as:
[tex]FD^2+EF^2=ED^2[/tex]
[tex]FD^2+22^2=36^2[/tex]
[tex]FD^2+484=1296[/tex]
[tex]FD^2=1296-484[/tex]
[tex]FD^2=812[/tex]
[tex]FD=\sqrt{812}[/tex]
[tex]FD=28.495613697\\\\FD\approx 28.5[/tex]
Therefore, length of side FD is approximately 28.5 units.
