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SAT Math 6.3 Geometry and Measurement 232 Views


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Description:

SAT Math 6.3 Geometry and Measurement

Language:
English Language

Transcript

00:02

Here’s your shmoop du jour, brought to you by the number 10.

00:06

Which is the biggest number we can count up to without removing our socks.

00:10

If an equilateral triangle has side length equal to 10, what is the length of its altitude?

00:16

Here are the potential answers...

00:22

Alright, down to business.

00:23

The altitude of a triangle always runs perpendicular to its base…

00:30

…and we can indeed see that a couple of right angles are formed at the bottom.

00:35

Which is dandy news.

00:37

Now we have ourselves a pair of right triangles.

00:39

We can deduce that the base of each right triangle is 5…

00:43

…since the length of each full side of the equilateral triangle is 10…

00:47

…and our altitude line bisects it.

00:49

Yup…slices it right down the middle…like that poor worm you disposed of in biology.

00:53

So…now that we have the length of two sides of our right triangle…

00:57

…5 for the base and 10 for the hypotenuse…

00:59

…we can apply our buddy Pythagoras and his theorem.

01:02

5 squared plus our altitude squared equals 10 squared.

01:06

Or… 25 plus our altitude squared equals 100.

01:10

So the altitude is going to be the square root of the difference,100 - 25, or 75.

01:16

Which simplifies to the square root of 25 times 3…

01:19

…or 5 square root of 3 and the answer is C.

01:22

Beautiful.

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