Notes for June 16

The interior angles of a triangle always add up to 180 degrees°.

There are two classification systems.

Largest angle classification

The measure of an obtuse angle x° is 180° > x° > 90°.
The measure of a right angle is 90° exactly.

The measure of an acute angle x° is 90° > x° > 0°.

Every triangle is exactly one of these three things.

Relationships between angles classification

An equilateral triangle has three equal angles, all of them measure 60°.
An isosceles triangle has at least two equal angles. What this means is equilateral is a special case of isosceles, the same way a square is a special case of a rectangle.
A scalene triangle's angles are all different from one another.

Defining a triangle by side lengths
 
If all we have are the angles, we have no idea about the area. For that, we need the sides lengths. Let's call the lengths u, v and w. Any three letters will do, but we are going to have a formula for area called Heron's Formula, and for that, we will need to reserve the letters p for perimeter and s for semi-perimeter. But before we get to that we have the triangle inequality. For three numbers to be the side lengths of a triangle we need

u + v  >=  w  >=  | u - v |


The last term is the absolute value of the difference between u and v. This is the cleanest way to put the information in an equation. In plain English, this says any two sides must add up to at least as much as the third side, and the easiest way to check that all of them are true is to see if the two short sides add up to more than or equal to the longest side.


Why did we make the inequality with greater than or equal to signs? Shouldn't just strictly be greater than?


No. If we have a case where the sum of the two short sides equals the long side, we have a degenerate triangle, which is a line segment with a dot on it. If we consider the simple area formula Area = ½ bh, a degenerate triangle has a height of zero, so the area is zero.

If we have the three sides, we don't have the height, so the simplest area formula is no good to us. Instead, we will use Heron's formula. Follow this link to see a few practice problems using Heron's formula.

  

Final exam

The link to the final is HERE.

It is due by noon. Send it to mhubbard@peralta.edu with MATH 50 FINAL in the subject line.

Good luck!
 

Practice exam for final

No class on Zoom today, but here is a link to a PRACTICE final exam.

The real final exam will be Wednesday, May 20, from 10:00 am to noon.

If you have questions, my office hour today will begin at 12:20 in Zoom room number 

584-656-357

Here is a link to the practice exam answers.

Answers to midterm 2

The answers can by found by clicking on this link.

If you are taking the final, it will be on Wednesday, May 20, from 10:00 am to noon.

in class midterm 2, due by 12:15 this afternoon

Here is the link to the in-class section of the exam.

Send both the take-home and the in-class to mhubbard@peralta.edu using the subject lines

Math 50 midterm 2 in-class [your name]

-or- 

Math 50 midterm 2 take-home [your name]

Answer sheet for Homework 10

Zoom recording for May 4

Link to the take-home section of Midterm 2, due by the end of class on Wed., May 6

Here is the link to the take-home section.

Homework 10 is due by midnight tonight.

In class, we will discuss changing the formulas for circles in Cartesian coordinates into  polar coordinates.

The in-class section will be given out at 11:00 am on Wednesday, due by 12:15 pm, which is also the deadline for the take-home section.

Here is a link to today's notes.

Answers to Quiz 6

Here is a link to the answer sheet for Quiz 6.

Link to Quiz 6

Click here for a link to Quiz 6. If you can, please finish by 12:15 and send to 

mhubbard@peralta.edu

Subject line: Math 50 quiz 6 [your name]
 

Link to homework 10

Click here for a link to Homework 10, due Monday, May 4

Answer sheet for Monday's homework

Click here for the answer key to Homework 9

Schedule for the next two weeks.

Homework 9 is due by midnight tonight.

Quiz 6 will be Wednesday in class for 20 points, based on Homework 9.

Homework 10 will be handed out on Wednesday, due next Monday.

Next week will be the second midterm. Take-home section will be handed out on Monday, due Wednesday, in class section on Wednesday.

Zoom room number is 114-391-513.
 

Answer sheet for Wednesday's quiz

Link to the answers. 

Quiz 5 was given in four parts over the last two weeks, you will be sent an email with your grades.

Homework 9, due next Monday, answers for Homework 8 and quizzes for today

Here is the link for Homework 9

Here is the link for the answers to Homework 8

Here is the link for the quiz if your last name starts with A through M 

Here is the link for the quiz if your last name starts with N through Z 

Link to Monday's lecture

Click here to see the lecture from Monday

Files for class on April 20

Click here for today's notes.

Click here for today's worksheet. Completing the work is worth 5 points toward the next quiz grade.

When you are finished with the worksheet, send an email with the answers to mhubbard@peralta.edu, I will send an answer sheet and grades of the students by tomorrow morning. Click here for the answer sheet.

Files for class on April 15

Link to the answers to Homework 7

Link to Homework 8, due Monday

Link to today's quiz. There are two pages, you only have to complete one, which one depending on the first letter of your last name.

Class at 11:00 today

The Zoom room number will remain the same for the rest of the term.

114-391-513

Please sign in with a name I will recognize.

See you this morning. I will be in the room at 10:50, class will start at 11:00.

Here is a link to the notes.
 
 

Both lectures and a link to the homework due Monday

The video of Monday's lecture

The video of Wednesday's lecture

Click this link for the homework.

See you soon, Stay safe.
 

Link to April 8 lecture on YouTube

Click here to go to the video.
 

Link to Homework 7, due Monday April 13

Click on this link for the homework.

If you want to follow along with today's lecture, click here.

YouTube link to yesterday's lecture (April 6)

https://www.youtube.com/watch?v=wkozZEwIh0Q

Notes for the week of April 6th and 8th

https://drive.google.com/file/d/16-F4fKvYJjHOP6HueN-9GPfDC_J0HTCT/view?usp=sharing

Above is the link to the notes used in the lecture about mathematical modeling with geometric and arithmetic sequences.
 

UPDATE: NEXT CLASS IS MONDAY, APRIL 6 AT 11:00 AM USING ZOOM SOFTWARE

You can access Zoom on a laptop or on a cellphone. The number for the class at 11:00 is
114-391-513
The number for the 12:20 office hour is
584-656-357
Hope to see you all this Monday.

Stay safe,
MattH
 

Face to face classes are canceled until Wednesday, April 8

No instruction, not face to face or online, will take place for the rest of the month.

Stay Safe,
Prof. Hubbard

Face to face classes are canceled for Wednesday, March 11

Laney has canceled face-to-face classes from Wednesday, March 11 to Saturday, March 14.
If you are enrolled in Math 50 and you read this, please send me an email at mhubbard@peralta.edu and include your student ID number.

Notes for Homework 5

Notes on decimal degrees, degrees/minutes/seconds (DMS), radians and radians written as multiples of pi

Notes for Homework 4

Notes on finding sine if you are given cosine. Once you find those, the other four trig function can be defined in terms of the first two. Also, notes on finding sine and cosine if you are given tangent.

Notes on changing from degrees to radians and vice versa.

Notes for Homework #3

Notes for getting rid of radicals in denominators of fractions

Notes for finding all six trig functions for an angle if you are given sine, cosine or tangent, assuming we are in Quadrant I

Notes for Homework #2

Notes for defining triangles by angles in degrees 

Notes for defining triangles by three points in the plane, finding the area and the classifications by finding the distances
 

Notes for Homework #1

Notes for defining triangles by side lengths.

Notes for degenerate triangles.

Notes for Heron's formula.
 

Degenerate triangles

The triangle inequality state that if the sides of a triangle are labeled a, b and c, we need two inequalities to be true a + b >= c >= |a - b|. If we get an equality, the triangle is said to be degenerate. For example, if the lengths are 9, 6 and 3, we would draw a line segment of length 9 with a point on the line splitting into two parts of length 6 and 3. To think of it in terms of base and height, the base would be 9 and the height 0, so the area would be zero.

There are some facts about degenerate triangles you should know.

a) If you plug in these values into Heron's formula, you will get an area of 0.

b) The angle sum is 180°, since there are angles of 180°, 0° and 0°. It is not truly obtuse, since 180° is a straight angle.

c) If the two short sides are equal, it qualifies as an isosceles triangle, if they are not equal, it is scalene.

d) When we define a triangle by three distinct points in the plane, we will get a degenerate triangle if the three points are all on the same line, which is known as colinear.