9514 1404 393
Answer:
4. 8 yds
5. 30 mi
Step-by-step explanation:
The relation according to the Pythagorean theorem is ...
c² = a² + b²
This can be solved for 'a' or 'b' to get ...
a = √(c² -b²)
b = √(c² -a²)
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4. b = √(17² -15²) = √(289 -225) = √64 = 8
The length of leg b is 8 yards.
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5. a = √(50² -40²) = √(2500 -1500) = √900 = 30
The length of leg 'a' is 30 mi.
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Additional comment
You may recognize the relevant Pythagorean triples as (3, 4, 5) and (8, 15, 17). A few others that are often seen are (5, 12, 13), (7, 24, 25) and (9, 40, 41). Any of these can be multiplied by some factor, as the (3, 4, 5) triple is in problem 5.
