Question

If b=24 and c=10 what is for the missing side a= ? by Use the Pythagorean Theorem to find

Answer 1

a = 21.82 if and only if b=10 and c=24

if you meant b=24 c=10

there can't be such a triangle because the hypotenuse is the longest side

Explanation:

`a^2+b^2=c^2\\\\a=?\\\\b=24\\\\c=10\\\\\\a^2+(24)^2=(10)^2\\\\a^2=(10)^2-(24)^2\\\\a^2=(10-24)(10+24)\\\\a^2=-14(34)`

which doesn't work because something squared can't be a negative

if you meant

c=24 and b=10

`a^2+(10)^2=(24)^2\\\\a^2=(24)^2-(10)^2\\\\a^2=(24-10)(24+10)\\\\a^2=(14)(34)\\\\a\approx 21.82`

Answer 2

9514 1404 393

Answer:

a = 26 or 21.82

Explanation:

If 'a' is the hypotenuse, then ...

a² = b² +c²

a² = 24² +10² = 576 +100 = 676

a = √676 = 26 . . . if 'a' is the hypotenuse

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If 'a' is the long side, then ...

b² = c² + a²

b² -c² = a² = 24² -10² = 576 -100 = 476

a = √476 ≈ 21.82 . . . if 'a' is the long leg

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Comment on the question

The problem statement doesn't tell us what side of the triangle is labeled 'a'. There are two possibilities. An answer has been provided for each. Use the one that applies to the figure you are given.