9-3 & 9-4

We learned the law of sine and the law of cosine this. I think that the law of cosine is much easier to do because you basically just plug all of your work into the calculator. It is hard to learn what formulas to use with which triangles. There is also SOHCAHTOA. You cannot use the law of cosine on a right triangle. The only time you can use it is when you do not have any pairs on a non - right triangle. Most of these start off with a word problem where you have to draw your own triangle, so it can get a little tricky.

The formula for law of cosine is (oppleg)^2 = (adjleg)^2 + (adjleg^2) – 2(adj leg) (adj leg) cos (angle between)

Ex : Suppose 2 sides of a triangle have lengths of 10cm and 8 cm and the angle between them measures to be 140 degrees. Find the 3rd side. Once you draw your triangle, you plug the numbers into the formula. X^2 = 10^2 + 8^2 – 2 (8)(10)cos140 The first step is to get rid of the squared on the x, so you square root it.The next step is to put it in your calculator. X= 96.281 ends up being your answer.

As i pretty much say in every blog Advanced Math is getting harder and harder. Everything you learn is accumulative and has to be remembered in order to solve other problems. Right now we are still in Chapter 9 working on triangles, which trigonometry is.

9-3 is all about the Law of Sines. The law of sine is only used with NON-RIGHT TRIANGLES. You are only about to use the law of sines when you have an angle and an opposite leg value that you know.

Formula: sin (angle) = sin (angle 2)
______________ _________________
opp leg opp leg 2

TIP: you must always cross multiply to solve.

Example: A civil engineer wants to determine the distances from points A to B to a inacessible point C. From direct measurement the engineer knows the AB=25cm AngleA=110° AngleB=20°. Find AC&BC

1.You draw out your triangle from what you already know. Once draw you see the you do not know legs a or b and AngleC.
2. To find angle c subtract the two angles known by 180°.
180-110-25=50°
3.Plug into formula..
sin50/25=sin110/AC
4.Cross multiply to get BCsin50=25sin10
5.Get BC by itself by dividing 50.
6. Answer for angle BC is 25sin110/sin50 which equals 30.667
-Next solve or AC-
1.ACsin50=25sin20
2.Divide to get AC alone.
3.Answer is 25sin20/sin50 which equals 11.162

Each problem is different but you always follow the same rules. Sometimes you may have to find angles, and don't forget when solving for an angle you do the inverse.

9-3

9-3 Law of Sines

Law of Sines is a method used to solve triangles that cannot be solved using SOHCAHTOA. Right now we are going to learn Law of Sines. Law of Sines is used with non right triangles. You can only use it if you have an angle and an opposite leg value you know. The formula to solve these triangles is: Sin(Angle)/Opposite Leg = Sin(Angle 2)/Opposite Leg 2 *Cross multiply to solve
Let’s try an example problem:

Example 1:
In triangle ABC angle B = 128°, side b = 14 and side c = 6. Determine whether or not angle C exists. If it does exist find all possible measures of angle C.

Sin 128°/14 = Sin C/6
6 Sin 14 = 14 Sin C
Sin C = 6 Sin 128°/14

At this point you will take the inverse = C = Sin-1(6 Sin 128°/14)
C = 72.435

Since you are taking the inverse you want two answers. So make your answer negative and add 180°.
-72.435 + 180 = 107.565

Your final answers are 72.435 & 107.565

9-2

We are in chapter nine in advanced math right now. In section 9-2, we learned how to find the area of a triangle given the lengths of two sides and the measure of the included angle. There are two formulas in this section – one for a right triangle and one for a non-right triangle.

1/2bh – only right triangles
1/2absin(angle b/w) – non right triangles

EXAMPLE 1: Two sides of a triangle have lengths 6 cm and 3 cm. The angle between the sides measures 70 degrees. Find the area of the triangle.
A). First, draw your triangle of course.
B). Label the two sides with 6 cm on one and 3 cm on the other.
C). Since we are not told it is a right triangle, we’re going to use the second formula
(1/2absin(angle b/w).
D). Plug in all of your numbers given. (1/2(6)(3)sin70 degrees)
E). Multiply to get 9sin70 degrees.
F). Your answer is A = 8.46 cm squared

EXAMPLE 2: In triangle ABC b=3, c=5, and a=60 degrees. Find the area.
A). Draw your triangle and label the sides.
B). Plug your numbers into the second formula, since we aren’t told it’s a 90 degree angle.
(1/2(3)(5)sin60 degrees).
C). Your answer is A = 6.5 *We aren’t given any units, so leave it alone.

Law of Sine and Cosine

This week in advanced math we started chapter 9, we learned law of sine and law of cosine. You may consider the law of cosine easier simply because after you have plugged all angles and sides into the formula you just plug that same formula into your calculator to get your answer. You must examine your problem very closely in order to know which law to use, be sure that all requirements of a formula are there in your triangle. It is hard to learn what formulas to use with which triangles. Along with law of sine and law of cosine there is SOHCAHTOA which involves a right triangle.

Law of Sines is used with a non-right triangle and an angle and opposite leg value that you know.
Formula: sin(angle) / opp leg = sin(angle 2) / opp leg 2
**cross multiply to solve

Ex 1: In triangleABC, angleS=126°, s= 12 and t=7 Determine whether angleT exists.
1.First draw and label the triangle.
2.Now we take our formula and plug our values into it.

Sin126°/12 = sinT/7 (multiply by 7 on each side)
7sin126°/12 =sinT
T= sinINVERSE(7sin126°/12)
T=28.159°

Law of Cosines is used when there is no pair in a non-right triangle.
Formula: (oppleg)^2 = (adjleg)^2 + (adjleg^2) – 2(adj leg) (adj leg) cos (angle between)

Ex 1: Suppose 2 sides of a triangle have lengths of 10cm and 8 cm and the angle between them measures to be 140 degrees. Find the 3rd side.

Once you draw your triangle, you plug the numbers into the formula.

X^2 = 10^2 + 8^2 – 2 (8)(10)cos140
Now we must square root the and the right side as well to get x.
Once that is done you can plug it into your calculator, make sure when you plug this into your calculator you put parenthesis.

And TADAAAAA X= 16.928

Chapter 9-4 Laws of Cosine

This week in Advance Math, the class learned the Laws of Sine and Cosine. I find the Law of Cosine to be much simpler and easier to comprehend because the majority of your work is done via calculator. The formulas are somewhat difficult and easy to confuse for one another. One method you can use is SOHCAHTOA(exclusive to right triangles). Law of cosine cannot be used for right triangles. it is only to be used on no right triangles without pairs.

The formula for law of cosine is (opp.leg)^2=(adj.leg)^2 + (adj.leg^2) - 2(adj. leg) (adj.leg) cos.

Ex:1 Two sides of the triangle have lengths of 12 cm and 6 cm and the angle between them measures to be 150 degrees. Find the 3rd side. Once you draw the triangle, plug in the numbers.

x^2=12^2 + 6^2- 2(6)(12)cos150.

step1: eliminate the squared x by taking the square root which leaves you with x.
step:2 plug into calculator

Answer(x):36

9-4 Law of Cosines

This week we learned the law of sine and the law of cosine. The law of cosine is much easier to do because you basically just plug all of your work into the calculator. It is hard to learn what formulas to use with which triangles. There is also SOHCAHTOA.

You cannot use the law of cosine on a right triangle. The only time you can use it is when you do not have any pairs on a non - right triangle.

Most of these start off with a word problem where you have to draw your own triangle, so it can get a little tricky. The formula for law of cosine is (oppleg)^2 = (adjleg)^2 + (adjleg^2) – 2(adj leg) (adj leg) cos (angle between)

Ex 1: Suppose 2 sides of a triangle have lengths of 10cm and 8 cm and the angle between them measures to be 140 degrees. Find the 3rd side.

Once you draw your triangle, you plug the numbers into the formula.

X^2 = 10^2 + 8^2 – 2 (8)(10)cos140

The first step is to get rid of the squared on the x, so you square root it.

The next step is to put it in your calculator.

X= 16.928 and that is your answer.