Tier 1 · geometry

Pythagorean

Right triangle: find missing side.

Files (1)

PYTHAG.py389 bytes

def p(s):print(s)
def o1():
 p("=FIND C=")
 a=float(input("a:"))
 b=float(input("b:"))
 c=(a*a+b*b)**0.5
 p("c="+str(c))
def o2():
 p("=FIND A=")
 a=float(input("a:"))
 c=float(input("c:"))
 b=(c*c-a*a)**0.5
 p("b="+str(b))
def menu():
 while True:
  p("=PYTHAG=")
  p("1:FIND C")
  p("2:FIND A")
  p("0:EXIT")
  c=input("?>")
  if c=="1":o1()
  elif c=="2":o2()
  elif c=="0":break
menu()

How to use it

Right-triangle solver. Pick your direction first:

1:FIND C — you know both legs, want the hypotenuse. Prompts a: and b:, returns c=√(a²+b²).
2:FIND A — you know one leg and the hypotenuse, want the other leg. Prompts a: (the known leg) and c: (hypotenuse), returns b=√(c²−a²).
0:EXIT — leave.

If a > c on option 2, you'll see a math error — re-check which side is the hypotenuse.

Example problem

A ladder leans against a wall. The foot is 5 ft from the wall and the ladder is 13 ft long. How high up the wall does it reach?

Hypotenuse is the ladder (c=13); one leg is the distance from the wall (a=5); we want the other leg (height up the wall).

Run PYTHAG, choose 2:FIND A.
a: → 5, c: → 13.
Output: b=12.0.

The ladder reaches 12 ft up the wall. Verify: 5² + 12² = 25 + 144 = 169 = 13². ✓

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Test cases (2)

ID	Inputs	Expected contains
3-4-to-5	1, 3, 4, 0	c=5.0
5-13-to-12	2, 5, 13, 0	b=12.0