Heights of Buildings and Other Hidden Shapes

Yo, everyone…. how’s the GED? I wanted to talk about somethin’ that came up in the GED Forum. Here’s a comment that Rick made:

I am struggling with the math as well. I live in MI and advanced algebra and calculus are required to pass. the thing here is that they make you take pre test before you are allowed to take the real test. And the pre test are unbelievable as well. Determining the height of a sky scraper by the time of day, direction of the sun, and the measurement of it’s shadow??? WTF!

Now, I don’t know exactly what question was on the test, but I know that the GED is famous for “hidden” shape questions. So, when you got a map, or a picture, or a diagram, or anything like that, you got to look for the shape in it. Look for circles, or paralell lines with a line crossing them, or (and here’s what I think’s happening here) RIGHT TRIANGLES. Man, the right triangle is yo’ friend, as soon as you can find one in a diagram, you probably got a pretty good idea what the question REALLY is.

Here was my response…

Hey, Rick! Does Michigan have its own test that’s different from the GED? Cuz the GED don’t really got no calculus on it. It’s got algebra and geometry, sure. And it’s got some confusing stuff.

Let me clue you in on the height-of-the-building idea. At least, I think I know what the question’s getting at, but if I’m wrong, see if you can remember more of the details, and I’ll see if I can hook you up with an answer.

A LOT of questions like that are really geometry questions about right triangles… the good old Pythagorean relationship. That says that one short side (leg) of a right triangle squared, plus the other short side (leg) squared, equals the long side (hypotenuse) squared.

Usually it’s written: a² + b² = c²

This formula is in the front of the GED test booklet. a and b are the sides that make a right angle (like a building and it’s shadow), and c is the long side (like from the end of the shadow to the top of the building).

So, when you’ve got a building and a shadow, the shadow and the building make two sides of a right triangle. You can draw an imaginary line from the end of the shadow to the top of the building to make the hypotenuse (c). If they give you c (the measure from the end of the shadow to the top of the building) and the length of the shadow (a), then you can figure out the height of the building (b).

Look for right triangles in any kind of diagram or map or question about height and distance. You can even use this to find the distance between two points on a graph. You’ll find it pretty much everywhere.

Let me know if you run into any word problems or diagrams that you can’t figure out what they’re REALLY asking for!

For more information about the GED test and GED test preparation, visit The GED Academy at http://www.passGED.com.