Question

100 POINTS! WILL MARK BRAINLIEST! WILL GIVE THANKS AND WILL R8! Also, I will report if you answer just for points!

Answer 1

Problem One
This is a right angle triangle. If it is not, then there is no way to do the problem. the right angle is across from the 19. 

Formula
a^2 + b^2 = c^2

Givens
a = 17
c = 19

Sub and solve
17^2 + b^2 = 19^2
289 + b^2 = 361  Subtract 289 from both sides.
b^2 = 361 - 289
b^2 = 72              Take the square root of both sides.
b = sqrt(72)          Factor 72
b = sqrt(6 * 6 * 2)  Take 6 outside the root sign.
b = 6*sqrt(2)

This is one possible answer b = 6*sqrt(2)
The other is a decimal          b = 6 * 1.414 = 8.485

Problem 2
Remark
If you are just counting units then the answer is 11 (miles). If you want an answer that goes the way a bird would fly directly to it then the problem will look like this.

Givens
Points (4,3) and (10,8)

Formula
d = sqrt( (y2 - y1)^2 + (x2 - x1)^2 )
y2 = 8
y1 = 3
x2 = 10
x1 = 4

Sub and solve
d = sqrt( (8 - 3)^2 + (10 - 4)^2 )
d = sqrt(  5^2 + 6^2)
d = sqrt(25 + 36)
d = sqrt(61)  Answer

That's one answer 
The other is the d = 7.8102 If you have choices show them please.