Warm Up 1.What is the Pythagorean Theorem (formula)? Solve for the missing side of each of the...
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![Page 1: Warm Up 1.What is the Pythagorean Theorem (formula)? Solve for the missing side of each of the following triangles: 2.3.4.](https://reader036.fdocuments.net/reader036/viewer/2022062407/56649e1b5503460f94b099f5/html5/thumbnails/1.jpg)
Warm Up1. What is the Pythagorean Theorem
(formula)?
Solve for the missing side of each of the following triangles:
2. 3. 4.
![Page 2: Warm Up 1.What is the Pythagorean Theorem (formula)? Solve for the missing side of each of the following triangles: 2.3.4.](https://reader036.fdocuments.net/reader036/viewer/2022062407/56649e1b5503460f94b099f5/html5/thumbnails/2.jpg)
Trigonometric
Ratios
A RATIO is a comparison of two numbers.
For example: boys to girls cats : dogs
right : wrong
In Trigonometry, the comparison is between
sides of a triangle.
![Page 3: Warm Up 1.What is the Pythagorean Theorem (formula)? Solve for the missing side of each of the following triangles: 2.3.4.](https://reader036.fdocuments.net/reader036/viewer/2022062407/56649e1b5503460f94b099f5/html5/thumbnails/3.jpg)
We need to do some housekeeping before we
can proceed…
![Page 4: Warm Up 1.What is the Pythagorean Theorem (formula)? Solve for the missing side of each of the following triangles: 2.3.4.](https://reader036.fdocuments.net/reader036/viewer/2022062407/56649e1b5503460f94b099f5/html5/thumbnails/4.jpg)
In trigonometry, the ratio we are talking about is the comparison of the sides of a
RIGHT TRIANGLE.
Two things MUST BE understood:1.This is the hypotenuse.. This will ALWAYS be the hypotenuse
2.This is 90°… WE WILL NEVER USE THIS ANGLE IN OUR CALCULATIONS!!!
![Page 5: Warm Up 1.What is the Pythagorean Theorem (formula)? Solve for the missing side of each of the following triangles: 2.3.4.](https://reader036.fdocuments.net/reader036/viewer/2022062407/56649e1b5503460f94b099f5/html5/thumbnails/5.jpg)
Now that we agree about the hypotenuse and right angle, there are only 4 things left; the 2 other
angles and the 2 other sides.
A We will refer to the sides in terms of their proximity to the angle
If we look at angle A, there is one side that is adjacent to it and the other side is opposite from it, and of course we have the hypotenuse.
opposite
adjacent
hypotenuse
![Page 6: Warm Up 1.What is the Pythagorean Theorem (formula)? Solve for the missing side of each of the following triangles: 2.3.4.](https://reader036.fdocuments.net/reader036/viewer/2022062407/56649e1b5503460f94b099f5/html5/thumbnails/6.jpg)
B
If we look at angle B, there is one side that is adjacent to it and the other side is opposite from it, and of course we have the hypotenuse.
opposite
adjacent
hypotenuse
![Page 7: Warm Up 1.What is the Pythagorean Theorem (formula)? Solve for the missing side of each of the following triangles: 2.3.4.](https://reader036.fdocuments.net/reader036/viewer/2022062407/56649e1b5503460f94b099f5/html5/thumbnails/7.jpg)
Remember we won’t use the right angle
X
![Page 8: Warm Up 1.What is the Pythagorean Theorem (formula)? Solve for the missing side of each of the following triangles: 2.3.4.](https://reader036.fdocuments.net/reader036/viewer/2022062407/56649e1b5503460f94b099f5/html5/thumbnails/8.jpg)
One more thing…
![Page 9: Warm Up 1.What is the Pythagorean Theorem (formula)? Solve for the missing side of each of the following triangles: 2.3.4.](https://reader036.fdocuments.net/reader036/viewer/2022062407/56649e1b5503460f94b099f5/html5/thumbnails/9.jpg)
Here we go!!!!
![Page 10: Warm Up 1.What is the Pythagorean Theorem (formula)? Solve for the missing side of each of the following triangles: 2.3.4.](https://reader036.fdocuments.net/reader036/viewer/2022062407/56649e1b5503460f94b099f5/html5/thumbnails/10.jpg)
Trigonometric Ratios
Name
“say” Sine Cosine Tangent
Abbreviation
Abbrev. Sin Cos Tan
Ratio of an angle
measure
sinθ = opposite side
hypotenuse
cosθ = adjacent side
hypotenuse
tanθ =opposite side
adjacent side
![Page 11: Warm Up 1.What is the Pythagorean Theorem (formula)? Solve for the missing side of each of the following triangles: 2.3.4.](https://reader036.fdocuments.net/reader036/viewer/2022062407/56649e1b5503460f94b099f5/html5/thumbnails/11.jpg)
One more time…Here are the ratios:
One more time…Here are the ratios:
sinθ = opposite side
hypotenuse
cosθ = adjacent side
hypotenuse
tanθ =opposite side
adjacent side
![Page 12: Warm Up 1.What is the Pythagorean Theorem (formula)? Solve for the missing side of each of the following triangles: 2.3.4.](https://reader036.fdocuments.net/reader036/viewer/2022062407/56649e1b5503460f94b099f5/html5/thumbnails/12.jpg)
Another House Keeping Note:
• We use lowercase letters to represent the sides of a triangle.
• We use uppercase letters to represent the angles of a triangle.
![Page 13: Warm Up 1.What is the Pythagorean Theorem (formula)? Solve for the missing side of each of the following triangles: 2.3.4.](https://reader036.fdocuments.net/reader036/viewer/2022062407/56649e1b5503460f94b099f5/html5/thumbnails/13.jpg)
Let’s practice…
B
c
a
C b A
Write the ratio for sin A
Sin A =
Write the ratio for cos A
Cos A =
Write the ratio for tan A
Tan A =
Let’s switch angles: Find the sin, cos and tan for Angle B:
Sin B =
Cos B =
Tan B =
![Page 14: Warm Up 1.What is the Pythagorean Theorem (formula)? Solve for the missing side of each of the following triangles: 2.3.4.](https://reader036.fdocuments.net/reader036/viewer/2022062407/56649e1b5503460f94b099f5/html5/thumbnails/14.jpg)
More Practice…
C
2cm
B A
3cm
Find an angle that has a tangent (ratio) of 2
3
![Page 15: Warm Up 1.What is the Pythagorean Theorem (formula)? Solve for the missing side of each of the following triangles: 2.3.4.](https://reader036.fdocuments.net/reader036/viewer/2022062407/56649e1b5503460f94b099f5/html5/thumbnails/15.jpg)
Even More Practice…
Find tan A: 24.19 12
A 21
Tan A =
8
4B
Tan B =
Find tan B:
![Page 16: Warm Up 1.What is the Pythagorean Theorem (formula)? Solve for the missing side of each of the following triangles: 2.3.4.](https://reader036.fdocuments.net/reader036/viewer/2022062407/56649e1b5503460f94b099f5/html5/thumbnails/16.jpg)
Evaluate the following:
1.Sin45 =
2.Cos56 =
3.Tan25 =