Grade 10 — Mathematics 10-3 › T3U05 The Pythagorean Theorem

Grade 10 › T3U05 The Pythagorean Theorem › L2
GRADE 10 · ALBERTAOUTCOME AB-MAT10-3-G2

L2 · Finding a missing side (A1: isolating a leg threaded)

Learning goal

“I can find the hypotenuse when I know both legs, and I can rearrange c^2 = a^2 + b^2 to find a missing LEG - subtracting before I take the square root (that rearrangement is the A1 skill: isolate the unknown by doing the same operation to both sides).”

Isolate — to get the unknown alone on one side of an equation by doing the same operation to both sides (preservation of equality).
Square root — the number that, multiplied by itself, gives the number under the root: √225 = 15 because 15 x 15 = 225. It undoes squaring.
Unknown side — the side whose length the problem asks for; it gets the letter (a, b or c) in the equation.
Substitution check — putting your answer back into a^2 + b^2 = c^2 to prove the areas balance.
Worked example

A right triangle has legs 9 m and 12 m. Find the hypotenuse. Step 1 (label first): the unknown is opposite the right angle, so it is c. Legs: a = 9, b = 12. Step 2 (EQUATION model): c^2 = a^2 + b^2 = 9^2 + 12^2 = 81 + 144 = 225. Step 3 (undo the square): c = √225 = 15 m. Step 4 (substitution check): 81 + 144 = 225, and 15 > 12 - the hypotenuse beats the longest leg, as it must. Say it plainly: for the hypotenuse, the moves are SQUARE, ADD, ROOT. The answer is never the sum of the legs (9 + 12 = 21 is the classic wrong turn).

Check yourself — explain it

c^2 = 225 is not the finished answer because...

Paired problem — example still visible

Legs 6 m and 8 m. Hypotenuse? -> c^2 = 36 + 64 = 100, c = 10 m

Faded completion — last step is yours

"Legs 5 cm and 12 cm: c^2 = 25 + 144 = ___, so c = √___ = ___ cm" -> 169; 169; 13 cm

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