Learn about the 3 main trig ratios and what it has to do with that summer camp you attended ages ago. 

Objective 1a

You will be able to discover and use the three main trig ratios

Camp Sohcahtoa? Counselors include Pythagoras and Ptolemy, and perhaps Plato.  But only to preserve the alliteration, because that guy mostly hangs around in dimly lit caves.  The other two guys will be demonstrating how trig ratios apply to the sides and angles of right triangles, while ensuring that Kenny doesn't drown in the lake.  Duration_10_36

Objective 1b

Using Geogebra, we construct a right triangle, and label the sides in reference to one of the acute angles: Opposite, Adjacent, and Hypotenuse.  Taking the ratio of any two of those will define one of the three main trig ratios.  Duration_9_43

Objective 1c

The previous video stopped just shy of actually figuring out which ratio of side lengths is sine, which is cosine, and which is tangent.  We will discover that now.  Duration_8_53

Objective 1d

Here is the summary of the sine, cosine, and tangent ratios, along with a couple of fun mnemonics to help you remember which ratio goes with what sides.  Duration_10_06

Objective 1e

If they wanted to find a particular trig value, what did scientists, mathematicians, and astrologers, I mean astronomers, do before the advent of the personal calculator?  They consulted a trig table, which was kind of like a log table, but not as natural.  Duration_14_25

Objective 1f

Just realized that we haven't actually solved for any missing side lengths using right triangle trigonometry.  Let's rectify that with these three examples.  Duration_13_08

Objective 1g

And finally, here are the worked-out solutions for your three independent practice problems.  Let's see how you did.  Duration_4_42

Geometry 7(B) apply the Angle-Angle criterion to verify similar triangles and apply the proportionality of the corresponding sides to solve problems. 

Geometry 9(A) determine the lengths of sides and measures of angles in a right triangle by applying the trigonometric ratios sine, cosine, and tangent to solve problems 

Geometry 9(B) apply the relationships in special right triangles 30º-60º-90º and 45º-45º-90º and the Pythagorean theorem, including Pythagorean triples, to solve problems