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Right Triangles. The Trig Ratios. Brought to you by Moody Mathematics. Let’s review some vocabulary. Moody Mathematics. A. Hypotenuse. C. B. Moody Mathematics. Opposite Leg. A. C. B. Opposite Leg to A. Moody Mathematics. Opposite Leg. Opposite Leg to B. B. Moody Mathematics. A.
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Right Triangles The Trig Ratios Brought to you by Moody Mathematics
Let’s review some vocabulary. Moody Mathematics
A Hypotenuse C B Moody Mathematics
Opposite Leg A C B Opposite Leg to A Moody Mathematics
Opposite Leg Opposite Leg to B B Moody Mathematics
A Adjacent Leg Adjacent Leg to A B Moody Mathematics
Adjacent Leg B Adjacent Leg to B Moody Mathematics
Consider the right triangles in this next slide: Moody Mathematics
What can you say about them? Moody Mathematics
They are similar By AA Moody Mathematics
They have the same right angle They have the same acute angle Moody Mathematics
All right triangles having one acute angle the same are similar. Moody Mathematics
For example, all 45-45-90 triangles are similar. Moody Mathematics
The legs of a 45-45-90 triangle are in a 1 to 1 ratio. Moody Mathematics
In a 45-45-90 triangle the ratio: leg hypotenuse Moody Mathematics
Also, all 30-60-90 triangles are similar. Moody Mathematics
In a 30-60-90 triangle, the ratio: leg opposite the 30o hypotenuse Moody Mathematics
The ratio: leg opposite the 600 hypotenuse Moody Mathematics
We have names for the 3 most common ratios that we will form in right triangles. Moody Mathematics
The names are: the Sine Ratio, the Cosine Ratio, the Tangent Ratio. Moody Mathematics
Sin A= Cos A= Tan A= Moody Mathematics
S O H – C A H – T O A “Some Old Hippy Caught Another Hippy Tripping On Antacid” Moody Mathematics
in SOH pposite ypotenuse Moody Mathematics
os CAH djacent ypotenuse Moody Mathematics
an TOA pposite djacent Moody Mathematics
Sin A = A Hypotenuse C B Opposite Leg to A Moody Mathematics
A Cos A = Hypotenuse Adjacent Leg to A B C Moody Mathematics
A Tan A= Adjacent Leg to A B Opposite Leg to A C Moody Mathematics
Now let’s set up the three ratios for angle B. Moody Mathematics
A Sin B= Hypotenuse Opposite Leg to B B C Moody Mathematics
Cos B = A Hypotenuse C B Adjacent Leg to B Moody Mathematics
A Tan B = Opposite Leg to B B Adjacent Leg to B C Moody Mathematics
Now let’s use a ratio to solve for a missing side of a right triangle: Moody Mathematics
Let’s estimate the value of x before we start: a. X>12 b. 6<x<12 c. X<6 A C B Moody Mathematics
It’s not (a) because A leg can’t be longer than the hypotenuse. a. X>12 b. 6<x<12 c. X<6 A C B Moody Mathematics
If B were 30o then x would be 6 exactly. Since B is smaller than 30o x<6. b. 6<x<12 c. X<6 A C B Moody Mathematics
Look at the parts involved and decide which ratio “fits” best. A C B Moody Mathematics
Where are the given and missing sides in relation to the known angle? A C B Moody Mathematics
X is the “opposite leg” to B and 12 is the “hypotenuse”. A C B Moody Mathematics
A C B Moody Mathematics
Now let’s use another ratio to solve for a missing side of a right triangle: Moody Mathematics
Let’s estimate the value of x before we start: a. X>16 b. 8<x<16 c. X<8 A B C Moody Mathematics
It’s not (a) because A leg can’t be longer than the hypotenuse. a. X>16 b. 8<x<16 c. X<8 A B C Moody Mathematics
If A were 30o then x would be 8. Since <A =55o is bigger than30o, x>8. b. 8<x<16 c. X<8 A B C Moody Mathematics
Look at the parts involved and decide which ratio “fits” best. A B C Moody Mathematics
Where are the given and missing sides in relation to the known angle? A B C Moody Mathematics
X is the “adjacent leg” to B and 16 is the “hypotenuse”. A B C Moody Mathematics
A B C Moody Mathematics
Now let’s solve another ratio to find a missing side of a right triangle, but this time x is on the bottom. Moody Mathematics
Look at the parts involved and decide which ratio “fits” best. A B C Moody Mathematics