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Nastasia [14]
3 years ago
5

How do you get an equation to solve for all 3 sides of a triangle?

Mathematics
2 answers:
slavikrds [6]3 years ago
7 0

In your solving toolbox (along with your pen, paper and calculator) you have these 3 equations:

1. The angles always add to 180°:

A + B + C = 180°

When you know two angles you can find the third.

 

2. Law of Sines (the Sine Rule):

Law of Sines

When there is an angle opposite a side, this equation comes to the rescue.

Note: angle A is opposite side a, B is opposite b, and C is opposite c.

 

3. Law of Cosines (the Cosine Rule):

Law of Cosines

This is the hardest to use (and remember) but it is sometimes needed  

to get you out of difficult situations.

It is an enhanced version of the Pythagoras Theorem that works  

on any triangle.

With those three equations you can solve any triangle (if it can be solved at all).

Six Different Types (More Detail)

There are SIX different types of puzzles you may need to solve. Get familiar with them:

1. AAA:

This means we are given all three angles of a triangle, but no sides.

AAA Triangle

AAA triangles are impossible to solve further since there are is nothing to show us size ... we know the shape but not how big it is.

We need to know at least one side to go further. See Solving "AAA" Triangles .

 

2. AAS

This mean we are given two angles of a triangle and one side, which is not the side adjacent to the two given angles.

AAS Triangle

Such a triangle can be solved by using Angles of a Triangle to find the other angle, and The Law of Sines to find each of the other two sides. See Solving "AAS" Triangles.

 

3. ASA

This means we are given two angles of a triangle and one side, which is the side adjacent to the two given angles.

ASA Triangle

In this case we find the third angle by using Angles of a Triangle, then use The Law of Sines to find each of the other two sides. See Solving "ASA" Triangles .

 

4. SAS

This means we are given two sides and the included angle.

SAS Triangle

For this type of triangle, we must use The Law of Cosines first to calculate the third side of the triangle; then we can use The Law of Sines to find one of the other two angles, and finally use Angles of a Triangle to find the last angle. See Solving "SAS" Triangles .

 

5. SSA

This means we are given two sides and one angle that is not the included angle.

SSA Triangle

In this case, use The Law of Sines first to find either one of the other two angles, then use Angles of a Triangle to find the third angle, then The Law of Sines again to find the final side. See Solving "SSA" Triangles .

 

6. SSS

This means we are given all three sides of a triangle, but no angles.

SSS Triangle

In this case, we have no choice. We must use The Law of Cosines first to find any one of the three angles, then we can use The Law of Sines (or use The Law of Cosines again) to find a second angle, and finally Angles of a Triangle to find the third angle.

trapecia [35]3 years ago
3 0

you would need to use the Law of Cosines for side then solve for .x,y, and z

Then simplify,

To solve for  use .

Solve and then round to the appropriate units

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Chelsea and her friends are making small fruit baskets for their neighbors. They have 90 pears, 45 peaches, and 75 apples. What
iVinArrow [24]

Answer:

15 baskets

Step-by-step explanation:

This question is a GCF question

The first step would be to find the factors of 45, 75 and 90

The factors of 45 are: 1, 3, 5, 9, 15, 45

The factors of 75 are: 1, 3, 5, 15, 25, 75

The factors of 90 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

The greatest common factor is 15.

Therefore, the greatest number of baskets they can make if each basket has the same number of pears, the same number of peaches, and same number of apples, with no fruit leftover is 15 baskets

3 0
2 years ago
If cos x=1/2 and 90°
Talja [164]

When I factor[ 2cos (square) - 5cos -3], I get (2cos + 1)(cos - 3). 2cos + 1 = 0, 2cos = -1, cos = -0.5,. Using inv cos on calculator, I get 120 degree related angle.

5 0
3 years ago
Hi please help i’ll give brain
Cloud [144]

Answer:

The GCF is going to be 30

Step-by-step explanation:

This Is how I find the GCF of 2 numbers. I find the prime factorization first, then I find the common factors and multiply them. Here

The prime factorization of 21, 2 × 3 × 3 × 5= 90

The prime factorization of 28, 2 × 3 × 5 × 7 = 210

The common factors are, 2, 3, and 5. We multiply those to get the GCF.

2 × 3 × 5 = 30

8 0
2 years ago
The points (12, 23) and (14, 45) lie on a line. What is<br> the slope of the line?
ozzi

Answer:

slope= 11

Step-by-step explanation:

(12,23) = (x1,y1)

(14,45) = (x2,y2)

Now,

slope(m)= (y2-y1)/(x2-x1)

=(45-23)/(14-12)

=22/2

=11

5 0
2 years ago
Can someone help me please? I don't understand this at all
Margarita [4]
X Is a number so ( x +12) a
6 0
2 years ago
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