Question

Angle FEDwith angleF=90degree, ED=36, and FE=22, calcularé the measures of the unknown angles and the unknown side length of the triangle. Round your measures to the nearest tenth of a degree

Answer 1

`\angle D=37.7^(\circ)`

`\angle E=52.3^(\circ)`

`FD\approx 28.5`

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:

`\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}`

`\text{sin}(D)=(22)/(36)`

`D=\text{sin}^(-1)((22)/(36))`

`D=37.66988696^(\circ)`

`D\approx 37.7^(\circ)`

Therefore, measure of angle D is 37.7 degrees.

Now, we will find measure of angle E using angle sum property.

`m\angle E+m\angle F+m\angle D=180^(\circ)`

`m\angle E+90^(\circ)+37.7^(\circ)=180^(\circ)`

`m\angle E+127.7^(\circ)=180^(\circ)`

`m\angle E+127.7^(\circ)-127.7^(\circ)=180^(\circ)-127.7^(\circ)`

`m\angle E=52.3^(\circ)`

Therefore, measure of angle E is 52.3 degrees.

We will use Pythagoras theorem to solve for side FD as:

`FD^2+EF^2=ED^2`

`FD^2+22^2=36^2`

`FD^2+484=1296`

`FD^2=1296-484`

`FD^2=812`

`FD=√(812)`

`FD=28.495613697\\\\FD\approx 28.5`

Therefore, length of side FD is approximately 28.5 units.