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Geometry and Measurement Videos 88 videos

SAT Math 2.1 Geometry and Measurement
2779 Views

SAT Math 2.1 Geometry and Measurement. What is the measure of angle z in terms of x and y?

SAT Math 1.1 Geometry and Measurement
719 Views

SAT Math 1.1 Geometry and Measurement. What is the circumference of the circle?

SAT Math 1.2 Geometry and Measurement
246 Views

SAT Math: Geometry and Measurement Drill 1, Problem 2. If A = (0, 4), B = (-3, 2), and C = (1, 0), which point is in the interior of angle ABC?

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SAT Math 3.4 Geometry and Measurement 213 Views


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Description:

SAT Math 3.4 Geometry and Measurement

Language:
English Language

Transcript

00:02

Here’s your shmoop du jour, brought to you by missing values.

00:06

Charles Manson could teach a master class on the subject.

00:10

What is the value of x in this figure?

00:12

And here are the potential answers...

00:15

Okay, so what we have here is a tale of two right triangles.

00:19

Let’s start with the bigger of the two.

00:21

The hypotenuse is 11…one leg is the dotted vertical line, or the height,

00:26

and the other leg is 6 plus x… whatever “x” is.

00:29

The smaller triangle has a hypotenuse of 7, the same height, and plain ol’ x as its base.

00:35

So, of course, because we’re dealing with triangles, we can use the

00:38

Pythagorean Theorem to solve for the missing leg, x

00:41

For the bigger triangle, (x + 6) squared + h squared = 11 squared.

00:47

For the smaller one, x squared + h squared = 7 squared.

00:51

We can simplify the second one a bit....

00:53

So now we have x squared + h squared = 49.

00:57

By subtracting x squared from both sides, we now have h squared = 49 - x squared…

01:02

…and we can now take the second part – the 49 minus x squared…

01:06

…and use it to replace the h squared in our first equation…

01:10

…giving us x squared + 12x + 36 + (49 - x squared) = 121.

01:23

We can add together our 36 and 49, like this…

01:26

…and our two x squareds cancel out…

01:27

…giving us 12x + 85 = 121.

01:30

We’ll knock 85 off both sides to get 12x = 36…

01:34

…and finally divide both sides by 12 to get x = 3.

01:38

Choice B.

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