Carrying Out Your Research Link

https://docs.google.com/spreadsheet/viewform?formkey=dDI0dWRUR1QwSGFUdlZVNFRYTDlnMXc6MQ

4.3 The Ambiguous Case of the Sine Law

On Friday, we started 4.3 and learnt Ambiguous cases. Ambiguous means unclear, unknown. An ambiguous case is a situation where two triangles can be drawn given the available information; the ambiguous case can occur when the given measurements are the lengths of two sides and the measure of an angle that is not contained by the two sides. (A.S.S. to remember).

We learnt that after you calculate 'h' using SOH CAH TOA you can determine how many triangles you can make. If 'h' is longer than the given side (5.5) you can only form 1 triangle. If 'h' is shorter than the length you calculated (3.5) you cannot form any triangles, and if the length of 'h' is in between what you calculated (3.5) and the given side (5.5) you can make 2 triangles.

To start solving an ambiguous case you have to:

1. Calculate the minimum length to make 1 triangle.

2. Compare minimum length to given length

This will show you the amount of triangles you will be able to make. Once you have completed this and two triangles can be made, you have to cr

eate two cases to show the two possibilities of what the triangle could look like using sine or cosine law, which we learnt in previous units.

The next person will be Brydon! :)

4.1 exploring the primary trigonometric ratios of obtuse angles

we did a chart and
sinx=sin(180-x)
cosx=cos(180-x)
tanx=tan(180-x)

There are relationships between the value of a primary trigonometri ratio for an acute angle and the value of the same primary trigonometric ratio for the supplement of the acute angle.

We used sin and cosine laws to determine the sine lengths and angle measures in acute oblique triangles.

the next person to write the blog is the person with the smallest hands

Bonus Problem!

The interior angles in a triangle are 120 degrees, 40 degrees, and 20 degrees.  The longest side of the triangle is 8 cm longer than the shortest side.  Determine the perimeter of the triangle to the nearest cm.

Complete and submit this problem before Wednesday, Nov. 2 to receive credit for it.  There is no penalty for not doing it, but if you will receive marks for getting it correct.

Project Link

Here is the link to the project form to fill out on Wednesday, October 26.

https://docs.google.com/spreadsheet/viewform?hl=en_US&formkey=dGg5QTE3d3A4OHpmMFFHLTVnTFNsZ0E6MQ#gid=0

Oblique Triangle Trigonometry

Today we started unit four. In this unit we will be learning the following:
-How to use sine law to determine side lengths and angle measures in obtuse triangles.
-How to use the cosine law to determine side lengths and angle measures in obtuse triangles.
-Solving problems that can be modelled using obtuse triangles.

In class we worked on a problem together. The problem is as follows:

On a dogleg hole, golfers have a choice between playing it safe and making the green in two shots or taking a chance and trying for the green in one shot. Jay can hit a ball between 170 and 190 yards from the tree with a 3-iron. Is it possible for Jay to make it to the green at this hole in one shot with a 3-iron? Explain.
This is the diagram we drew:

We figured out what side “a” was by using cosine law.
a(squared)= 51(squared) + 160(squared) - 2(51)(160) cos110
a=184 yrds.

Therefore, yes he could make it to the green in one shot.

After that, we filled in the chart on page 162 and compared our answers with a partner.
Next is Allysa! (:
By Kelsey.

Solving Problems Using Acute Triangles

Today we used the cosine law hte sine law and the primary trigonometric ratios to figure out the side lengths angle angle measures of acute triangles. we did an example in class where manuel wanted to see how high the worlds tallest free-standing totum pole was. Manuel walked out how far the shadow was 42m and then saw the angle of elevation of the sun was 40 degrees. Manuel realized there was a 5 degree slope to the ground. he found the angle at the base of the totum pole was 85 degrees and that the other angle to the ground was 45 degrees he then found the third angle to be 50 degrees using sine law he found the height to be 38.768m tall










next will be Allysa

By: Brydon

Today in class we continued learning about the sin law. Also we learnt about cos sin law. We looked over the books examples on pg. 132,133 and examined the formula for cos sin law.

next is: who ever hasn't done one yet

Proving and Applying the Sine Law

Today we learned about the sin law, which can be used to determine unknown side lengths or angle measure in acute angles. To use the sin law you need to know either two side lengths and a angle opposite to a known side, or two angles or any side. If you know the measure of two angles in a triangle, you can determine the third angle because all triangles have to add up to 180. We used the formulas shown below to find all unknown angles and side length.

We we went through the examples on pages 118-123 to get more of a clearifiactaion as to how to use the formulas.

We finished class off with an assignment on page 125.

Next will be Tanner! :)

Chapter 3

today we needed a calculator.

at the beginning of class we looked at a picture of an acute triangle over an area of land. as a class we determined that someone such as a geographer or pilot would need to know the exact distances of this triangle between cities.

as a class we also decided that a triangle must be a right triangle to directly use triganometry ratios.

we then did the lacrosse problem on page 114.

We found that you must add a line segment to use trig ratios. We split the 6 ft line in half and joined it with the vertex across from it. We now formed two 90 degree angles. We then used sine to find the length of the unknown side. We continued by using trig and found that the goal was 5.43 feet. ... We were wrong. The answer is still unknown.

We then did our chapter 3 diagnostic test.

Next will be the girl who sits beside me.
:)

2.4 angle properties in polygons

key idea....

• you can prove properties of angles in polgons using other angle properties that have already been proved

need to know

• the sum of the measures of the interior angles of a convex polygon with N sides can be expressed as 180 degrees(n-2)


• the measure of each interior angle of a regular polygon is 180 (n-2)

_____

n

• the sum of the measures of the exterior angles of any convex polygon is 360 degrees

ex: if a polygon has 15 sides what is the sum of the interior angles

answer: 15-2=13

13x180=2340

2340/15=156

answer is 156

next is sarah donald!!!

this is finally my post :)

Angle Properties in Polygons

we learned how to find the sum of interior angles using (s-2)180. This only works with convex polygons not concave, to be convex no angles can be bigger than 180

We also learned about the sum of exterior angles, as shown in the diagram below

w=180-A

x=180-b

y=180-c

z=180-d

s=w+x+y+Z = (180-a)+(18o-b)+(180-c)+(18o-d)= 720-a-b-c-d

720 -1(a+b+C+D)

720-360= 360

this is how we found out the exterior angle sum for this 4 sided figure.

next is stelzer
Drawing and painting online tool

Math 20 Foundations Exam

This week will be a busy week in Math Foundations 20.

On Wednesday, Oct. 5 we will write a Practice Exam for Chapter 2.

On Thursday we will be in the Writing Lab. We will work on our Logo Design Assignment (Chapter Task 2) and also select a topic for our Course Project. The Logo Design task is due on Tuesday after the long weekend, October 11.

On Friday, October 7 we will be writing the Chapter 2 Exam.

Have a great week. If you need any extra help, come and see me!

Long-Awaited Thursday Post (Now With More Friday!)

On Thursday, the class didn't do much. We took sheets of paper and drew straight lines from two of the vertices to a point on the opposite side of the paper, then cut them out, creating two right triangles and one acute triangle (Oooh facinating). We noticed that when we put the two right angled triangles on the bigger accute triangle, they matched up the same. Using our knowledge of supplementary and alternate angles, we were able to figure that the sum of the interior angles of any triangle equals 180 degrees (Wow what magic!)
On Friday we talked about non-adjacent interior angles (Sounds fun)! Non- adjacent Interior Angles are two angles of a triangle that do not have the same vertex as an exterior angle. In the picture, angle X and angle Y are non-adjacent interior angles to angle Z! We discovered that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non- adjacent interior angles (which is pretty cool because it shows the neat relations between the sides of a triangle!). We had an assignment to do and it was page 90, #1-3, 5, 6, 8, 9, and 12! Big assignment, but I'm sure we all got it done, RIIIIIGHT??

Next up is Colby!!