So we’ve become experts in finding and sketching angles and reference triangles, but what are they good for?
How do people use Reference Angles and Triangles in real life?
Right Triangles are used in all types of architecture. You see them every time you climb stairs, look at a roof, or cross over a bridge.
You see triangles in kites, skateboard ramps, street signs, airplanes, sailboats, and even mountains.
And, haven’t you ever eaten a sandwich that was first cut into two triangles? Mmmmm, food!
Gosh, triangles are everywhere!
Did you know that you create triangles and use math with your eyes every single day!
Every time you look up at something in the sky, you are creating something called the Angle of Elevation with your eyes. Moreover, when you look down at something on the ground, you are creating an angle called Angle of Depression.
Neat!
Angle of Elevation
Well, trigonometric functions are used to calculate distances by finding an angle determined by a horizontal (x-axis) and a line of sight (hypotenuse).
When we “elevate” our eyes to look up at the top of a building or see a bird in the sky we create an angle with the ground that we can then use to calculate the height or even the distance away from whatever it is we are looking toward. You never know when you might need to calculate the height of a saguaro cactus while driving through Arizona, as Purple Math beautifully illustrates.
Finding lengths and angles of a Right Triangle
The same thing can be said when we look down (i.e., we “depress” our eyes). We create right triangles all around us that will help us to find distances and angles.
So, let’s use our power of trigonometry and right triangles to calculate the distances of things we see all around us particularly, what you see above you and below you, as Khan Academy illustrates.
In this lesson we are not only are we going to use our knowledge of right triangles (i.e., Pythagorean Theorem and SOH-CAH-TOA), but we are going to draw upon our knowledge of geometry, once again, and use the power of alternate interior angles to help us solve some pretty cool problems such as:
- The distance from a radar station to a plane
- The distance from a buoy to a lighthouse
- The distance between two boats out at sea
- And more
Angles of Elevation and Depression – Video
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