The length of EF in the given triangle is 8.80 m.
Step-by-step explanation:
Step 1:
In the given triangle, the opposite side's length is 16.2 m, the adjacent side's length is x m while the triangle's hypotenuse measures 16.2 m units.
The angle given is 90°, this makes the triangle a right-angled triangle.
So first we calculate the angle of E and use that to find x.
Step 2:
As we have the values of the length of the opposite side and the hypotenuse, we can calculate the sine of the angle to determine the value of the angle of E.
[tex]sinE = \frac{oppositeside}{hypotenuse} =\frac{13.6}{16.2} = 0.8395.[/tex]
[tex]E = sin^{-1} (0.8395), E = 57.087.[/tex]
So the angle E of the triangle DEF is 57.087°.
Step 3:
As we have the values of the angle and the hypotenuse, we can calculate the cos of the angle to determine x.
[tex]cos E = \frac{adjacentside}{hypotenuse} = \frac{x}{16.2} .[/tex]
[tex]cos(57.087) = 0.5433, x = 16.2 (0.5433) = 8.8014.[/tex]
Rounding this off to the nearest hundredth, we get x = 8.80 m.
