In this lesson:
By the end of this lesson, you should be able to:
A TV's diagonal, a leaning ladder, a slanted path — each hides a right triangle.
Legs 6 and 8: , so .
When you know both legs:
Square each leg, add, then take the square root.
When you know the hypotenuse and one leg: . Subtract, then root.
Legs 3 and 7:
is exact; is the decimal approximation.
Hypotenuse 13, leg 5:
Check: . Confirmed.
Hypotenuse 10, leg 4:
Memorize these — and any multiple works too, like --.
Before solving, ask: am I finding the hypotenuse (add) or a leg (subtract)?
A negative under the root means you swapped the hypotenuse and a leg.
Most problems don't draw the triangle. Use the three-step cycle:
A 48-by-36 screen: inches.
Drop the altitude: it bisects the base. .
feet.
A hiker walks 600 m east, then 800 m north.
A wire runs from the top of a 24-ft pole to a point 10 ft from its base.
The wire is the hypotenuse. Set up and solve before advancing.
A student writes: "Legs 3 and 4, so the hypotenuse is ."
What did they do wrong? What is the correct answer?
A baseball diamond is a square, 90 ft on each side.
Find the distance from home plate to second base. No diagram given — draw it yourself.
✓ Hypotenuse: add then root. Leg: subtract then root ✓ Real problems: draw, extract the right triangle, then solve Never just add the sides — and check which side is the hypotenuse
Next: the same idea, lifted into three dimensions.
Click to begin the narrated lesson
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles