Answer:

Step-by-step explanation:
A right triangle is formed.
300 miles and 400 miles are the legs of the triangle.
We can apply Pythagorean theorem.




Answer:
Karen is 71 years old
Step-by-step explanation:
Known
Karen=Jack +35
Frank=1/2 Jack
Jenifer=Frank+17
If Jenifer=35
35=Frank+17
18 = Frank
18=1/2 Jack
36= Jack
Karen= Jack+35=36+35=71
Observe attached picture.
On picture we have:
A = height of flagpole = x ft
B = length of flagpole's shadow = 24 ft
C = height of sign = 6 ft
D = length of sign's shadow = 3 ft
When we draw a picture representing this problem we can also add another line marked in red. This way we can see that we have two right-angle triangles. We can see that both have same angle marked with α.
We can apply trigonometry rules to find height of flagpole.
From small triangle containing sign we can find tangens function:

Similarly we can do for large triangle containing flagpole:

We see that these two equations have same left sides. This means that their right sides must also be same:

We can solve for A:

Height of flagpole is 48 feet.
Hello friend ,. I hope it's helps you
enjoy your day
It equals 0.0192727261287227 mathamatics