For the given triangle, DE = 6.97 units.
Step-by-step explanation:
Step 1:
In the given triangle, the angle is 55°. The adjacent side has a length of 4 units and assume the hypotenuse, DE measures x units.
To calculate the value of x, we determine the cos of the triangle where we divide the length of the adjacent side by the length of the hypotenuse.
[tex]cos \theta = \frac{adjacentside}{hypotenuse}.[/tex]
Step 2:
The length of the adjacent side = 4 units.
The length of the hypotenuse = x units.
The angle of the triangle = 55°.
[tex]cos \theta = \frac{adjacentside}{hypotenuse}, cos 55 = \frac{4}{x}, cos 55 = 0.5735.[/tex]
[tex]x = \frac{4}{0.5735} = 6.9747.[/tex]
So x = DE = 6.9747 units, rounding this off to the nearest hundredth we get DE = 6.97 units.
