By the Pythagorean theorem
50^2 = x^2 +(x +34)^2
2500 = 2x^2 +68x + 1156
x^2 +34x -672 = 0
(x -14)(x +48) = 0
x = 14 or -48
The distance from the wall to the base of the ladder is 14 ft.
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7-24-25 is a Pythagorean triple. The dimensions here are double those values. It can be handy to know a few of the Pythagorean triples, as that can let you write down the answers to problems without having to go through the equations.
Answer:
1) Newbury Park → The distance is accurate.
2) Thousand Oaks → The distance is not accurate.
3) Los Angeles → The distance is not accurate.
Step-by-step explanation:
It is important to remember that:

Knowing this, you can make the corresponding conversions:
1) Newbury Park
10 miles to kilometers:
The distance shown in that California highway sign is accurate.
2) Thousand Oaks
13 miles to kilometers:
The distance shown in that California highway sign is not accurate.
3) Los Angeles
55 miles to kilometers:
The distance shown in that California highway sign is not accurate.