Answer:
D. 10.2
Step-by-step explanation:
Since the triangle is a right triangle we can use the Pythagorean theorem.
I will call the hypotenuse [tex]h[/tex], so in this case:
[tex]h=19[/tex]
and one leg will be [tex]l[/tex], in this case:
[tex]l=16[/tex]
and the unknown for this problem is the other leg which in the image is called [tex]x[/tex].
So the formula for the  Pythagorean theorem:
[tex]h^2=l^2+x^2[/tex]
clearing for x:
[tex]x^2=h^2-l^2\\x=\sqrt{h^2-l^2}[/tex]
substituting [tex]h=19[/tex] and [tex]l=16[/tex]:
[tex]x=\sqrt{19^2-16^2}\\ x=\sqrt{361-256}\\ x=\sqrt{105}\\ x=10.2[/tex]
the value of x is option D. 10.2
