Step 1:
Concept: Name the given sides and use the Pythagoras theorem to solve for DE.
Step 2:
The side facing the right angle is the hypotenuse = DF
The side facing the given angle is the opposite = DE
The third side is the adjacent = 6
Step 3: Apply the Pythagoras theorem.
[tex]\begin{gathered} \tan \text{ }\theta\text{ = }\frac{opposite}{\text{adjacent}} \\ \tan \text{ 50 = }\frac{DE}{6} \\ 1.192\text{ = }\frac{DE}{6} \\ DE\text{ = 1.192 }\times\text{ 6} \\ DE\text{ = 7.152} \end{gathered}[/tex]
Final answer
DE = 7.152
