http://us.cdn3.123rf.com/168nwm/argument/argument0901/argument090100156/4205169-young-woman-on-the-edge-of-petersburg-s-roof.jpg
a) What is the height between her eyes to the top of the building?
b) What is the angle of depression?
Solution:
Wednesday, March 5, 2014
WPP#12: Unit O Concept 10: How to Solve Depression and Elevation Word Problems
a) What is the height between her eyes to the top of the building?
b) What is the angle of depression?
Solution:
Tuesday, March 4, 2014
I/D2: Unit O- How to Derive Special Right Triangles
Inquiry Activity
1. Deriving a 45-45-90 triangle
Click Here
2. Deriving a 30-60-90 triangle
Click Here
3. The reason why both of these the 30-6-90 triangle and the 45-45-90 triangle have variables of "n" and not just the numbers because there is a relationship between as to why these numbers are there and they end up being a patter for all triangles of that kind. The variables make it a rule and make it true for all the special right triangles.
Inquiry Activity Reflection
1.Something I never noticed about special right triangles is... that all the sides have a pattern that is common between that type of right triangle. For example, In a 45-45-90 triangle we know that "a" and "b" will be the same since they have the same angle value. The hypotenuse however has an extra radical 2 being multiplied to the value of both "a" and "b". For a 30-60-90 triangle we see that the length of the shortest side which could be classified as "a" has a value of n. The value of the medium size side is n radical 3, and the side of the hypotenuse is 2n. Which makes since we see that the hypotenuse is suppose to be greater since it is the longest side and it is in the equation.
2. Being able to derive these patterns myself aid in my learning because... it helps me understand how everything connects and allows me to fully understand how to solve each and every problem. This can be very important to me in the long run because if i ever forget the rules i can easily derive them using the Pythagorean theorem and will help me connect everything else to the unit circle and not just with a radius (hypotenuse) of 1 but of any number and can solve it.
1. Deriving a 45-45-90 triangle
Click Here
2. Deriving a 30-60-90 triangle
Click Here
3. The reason why both of these the 30-6-90 triangle and the 45-45-90 triangle have variables of "n" and not just the numbers because there is a relationship between as to why these numbers are there and they end up being a patter for all triangles of that kind. The variables make it a rule and make it true for all the special right triangles.
Inquiry Activity Reflection
1.Something I never noticed about special right triangles is... that all the sides have a pattern that is common between that type of right triangle. For example, In a 45-45-90 triangle we know that "a" and "b" will be the same since they have the same angle value. The hypotenuse however has an extra radical 2 being multiplied to the value of both "a" and "b". For a 30-60-90 triangle we see that the length of the shortest side which could be classified as "a" has a value of n. The value of the medium size side is n radical 3, and the side of the hypotenuse is 2n. Which makes since we see that the hypotenuse is suppose to be greater since it is the longest side and it is in the equation.
2. Being able to derive these patterns myself aid in my learning because... it helps me understand how everything connects and allows me to fully understand how to solve each and every problem. This can be very important to me in the long run because if i ever forget the rules i can easily derive them using the Pythagorean theorem and will help me connect everything else to the unit circle and not just with a radius (hypotenuse) of 1 but of any number and can solve it.
Friday, February 21, 2014
I/D #1: Unit N Concept 7-9 : Applications of a right triangle apply to the creation of the unit circle
Inquiry Activity Summary
1. Video on how to find a 30 60 90 triangle.
2. Video on 45 45 90
The values of r( hypotenuse ) is 1, the value of x(horizontal) is radical 2 divided by 2 , and y(vertical) is also radical 2 divided by 2.
3. Video on 60 30 90 triangle
4. This activity helps derive the unit circle by being able to just focus on one quadrant and then realizing that there are only certain things that change. This also helps see what the unit circle consists of, where we get our points from (the coordinates) and how everything eventually ends up changing just by the sign. This activity helped me understand what each coordinate meant on the unit circle by just focusing on one part and then managing to move what I have learned and understand why and how it changes.
5.How does everything tie together?
The sides for the 30 degree triangle will still be r=1 x=radical 3/2 and y= 1/2. For the 45 degree triangle r=1 y=radical 2 divided by 2 and y= radical 2 divided by 2. The 60 degree triangle will be r=1 y=1/2 and x= radical 3 over 2.
Inquiry Activity Reflection
1. The coolest thing i learned from this activity is how to connect everything that we have learned in previous years to what is essential to learn now.
2. This activity will help me in this unit because it is the foundation as to where the unit circle comes from and the rational behind it. Which means that if i were to ever forget what the unit circle is i would be able to solve it and not just remember nonsense. This is also essential because these are the most important points of the unit circle that repeat throughout.
3.Something that i never realized before about special right triangles and the unit circle is that they actually have a relation between them. The entire unit circle consist of numerous right triangles that give it its coordinates. Without the special right triangle this would not be accurate or as easy to manage as it is now. The special right triangles are the fundamental aspects of the Unit Circle.
1. Video on how to find a 30 60 90 triangle.
2. Video on 45 45 90
The values of r( hypotenuse ) is 1, the value of x(horizontal) is radical 2 divided by 2 , and y(vertical) is also radical 2 divided by 2.
3. Video on 60 30 90 triangle
4. This activity helps derive the unit circle by being able to just focus on one quadrant and then realizing that there are only certain things that change. This also helps see what the unit circle consists of, where we get our points from (the coordinates) and how everything eventually ends up changing just by the sign. This activity helped me understand what each coordinate meant on the unit circle by just focusing on one part and then managing to move what I have learned and understand why and how it changes.
5.How does everything tie together?
The sides for the 30 degree triangle will still be r=1 x=radical 3/2 and y= 1/2. For the 45 degree triangle r=1 y=radical 2 divided by 2 and y= radical 2 divided by 2. The 60 degree triangle will be r=1 y=1/2 and x= radical 3 over 2.
Inquiry Activity Reflection
1. The coolest thing i learned from this activity is how to connect everything that we have learned in previous years to what is essential to learn now.
2. This activity will help me in this unit because it is the foundation as to where the unit circle comes from and the rational behind it. Which means that if i were to ever forget what the unit circle is i would be able to solve it and not just remember nonsense. This is also essential because these are the most important points of the unit circle that repeat throughout.
3.Something that i never realized before about special right triangles and the unit circle is that they actually have a relation between them. The entire unit circle consist of numerous right triangles that give it its coordinates. Without the special right triangle this would not be accurate or as easy to manage as it is now. The special right triangles are the fundamental aspects of the Unit Circle.
Monday, February 10, 2014
RWA #1: Unit M Concept 5 : Ellipse the Life Application
1. Definition: "The set of all points such of the sum of the distance from two points known as a foci is a constant." ( Mrs. Kirch)
2. Algebraic Equation:
(X-h)^2/a^2 + (y-k)^2/b^2=1 (horizontal)
(http://theo.x10hosting.com/examples/Ellipse/Ellipse6.jpg)
(x-h)^2/b^2 + -k)^2/a^2=1 (vertical)
(http://theo.x10hosting.com/examples/Ellipse/Ellipse7.jpg)
There are some very important key parts that an ellipse contains which are what defines it. There is a major axis, minor axis, foci and co-foci, vertices, and a center. These components are the components of an ellipse.
As we can see the graphs vary depending on where the greater value is. a must be the value of the greatest denominator. We see that the further away the foci is from the end point the skinnier the graph gets. The closer the foci is from the end point the skinnier the graph gets. The foci always lies under the major axis.
For more information on Ellipses see click this link http://www.purplemath.com/modules/ellipse.htm
#4 Real World Application: There are various components to Form an Ellipse. The standard form of an ellipse must have a plus sign in between the two terms and must be set equal to 1.To find out if the graph will be fat or skinny then we have to see what the transverse axis is, if the greater number is under "x" then it will be a fat ellipse of the grater number is under "y" then it will be a skinny ellipse. The transverse axis is equal to 2a which is the measure from one vertice to the other. To find "a" we take the distance between the center and one vertice. The Major axis contains "a", "c" and The center. The minor axis contains "b" and the center. To find "b" we know that it is the distance between one co-vertice to the center. To find the eccentricity of an ellipse we use c/a which should be 0>e<1.
Video:This demonstrates the shape tgat the earth goea around using the un to be its point of orbitibg. The planets go around the sun so it serves as their main focus to help them stay balanced. The position of the sun depends on which planet is orbiting. However the the sun if the part that all the planets revolve around just like the center would be for an ellipse.
#4 Work cited
google.com
youtube.com
kirchmathanalysis.blogspot.com
wikipedia.org
2. Algebraic Equation:
(X-h)^2/a^2 + (y-k)^2/b^2=1 (horizontal)
(x-h)^2/b^2 + -k)^2/a^2=1 (vertical)
(http://theo.x10hosting.com/examples/Ellipse/Ellipse7.jpg)
There are some very important key parts that an ellipse contains which are what defines it. There is a major axis, minor axis, foci and co-foci, vertices, and a center. These components are the components of an ellipse.
As we can see the graphs vary depending on where the greater value is. a must be the value of the greatest denominator. We see that the further away the foci is from the end point the skinnier the graph gets. The closer the foci is from the end point the skinnier the graph gets. The foci always lies under the major axis.
For more information on Ellipses see click this link http://www.purplemath.com/modules/ellipse.htm
#4 Real World Application: There are various components to Form an Ellipse. The standard form of an ellipse must have a plus sign in between the two terms and must be set equal to 1.To find out if the graph will be fat or skinny then we have to see what the transverse axis is, if the greater number is under "x" then it will be a fat ellipse of the grater number is under "y" then it will be a skinny ellipse. The transverse axis is equal to 2a which is the measure from one vertice to the other. To find "a" we take the distance between the center and one vertice. The Major axis contains "a", "c" and The center. The minor axis contains "b" and the center. To find "b" we know that it is the distance between one co-vertice to the center. To find the eccentricity of an ellipse we use c/a which should be 0>e<1.
(http://t0.gstatic.com/images?q=tbn:ANd9GcSrxcN_F6b6JjbiOJo-VBDHOTMXGdT_Ddr9Arm8kSI8VXNSRz2s8oc5ltfl)
This is a demonstration as to how ellipsis apply to the real world. The orbit of the planets consists of elliptical orbits. The sun is used as the center of the ellipse that all the planets have. The further away from the planet is the greater its foci will be. In order for everythibg to stay in balance tge eccentricity of each ellipse should be greater than 0 but les than one. The orbit of the planets must be in this shape or else the elements will be unbablanced which will
Video:This demonstrates the shape tgat the earth goea around using the un to be its point of orbitibg. The planets go around the sun so it serves as their main focus to help them stay balanced. The position of the sun depends on which planet is orbiting. However the the sun if the part that all the planets revolve around just like the center would be for an ellipse.
#4 Work cited
google.com
youtube.com
kirchmathanalysis.blogspot.com
wikipedia.org
Friday, January 10, 2014
Tuesday, December 17, 2013
WPP9: UNIT L concepts 4-8- Combination and Permutations; The delectable, Delicious Pizzeria
Create your own Playlist on MentorMob!
Sunday, December 8, 2013
SP6: unit K concept 10- repeatibg decimal to a rational number
Thank you. I hoped this helped :D
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