Pythagorean Theorem

Pythagorean Theorem

Pythagoras was a teacher in ancient Greece.

• Pythagoras was a teacher of many subjects including music & the new math called “geometry”.

He is credited with proving a certain fact…

• In any right triangle, if you make squares out of the shorter sides and add their areas, it equals the area of a square made with the longest side.

b

a c

“HYPOTENUSE”

a a

“LEGS”

c b

b

Either one can be labeled “a” or “b”

This side is ALWAYS labeled “c”

If you add the square of “a” and the square of “b” you get the square of “c”

a² + b² = c²

Pythagorean Theorem: for any right triangle, the squares of the shorter sides added equals the square of the longest side.

a² + b² = c²

If we know two of the sides of a right triangle, we can find the length of the third side with this formula!

c5

3 4

a² + b² = c² (3)² + (4)² = c² 9 + 16 = c² 25 = c² -5 or 5 = c

This formula is useful, especially in construction…

a²got+ ab² =ladder, c² You 50ft 15 ft from a building. (15)² + b² = (50)² How far up does the ladder reach? 225 + b² = 2500

50 ft.

?

-225

-225 b² = 2275 b = 47.7 ft.

15 ft.

100 ft

50 ft.

?

The top beam of a bridge is 100 ft. The exact middle vertical support is 50 ft. How long must you make the diagonal?

You You Your see know .30-06 Bambi the has ridge ona arange is about of ridge. 300 yards when shooting up. 200 yards elevation from you, and about 300 yards away.

a² + b² = c²

? 200 yds

300 yds