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Solving Triangles
law of sines, cosines, triangles, sohcahtoa
21
Mathematics
12th Grade
11/19/2014

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Cards

Term
List three Pythagorean identities
Definition
1. sin^2 Ɵ + cos^2 Ɵ =1
2. tan^2 Ɵ +1= sec^2 Ɵ
3. cot^2 Ɵ +1= csc^2 Ɵ
Term
what is SOH CAH TOA
Definition
SOH: sin=opp/hyp
CAH: cos=adj/hyp
TOA: tan=opp/adj
Term
What are the cofuntions? sin30= tan40= sec80=
Definition
sin30=cos60 tan40=cot50 sec80=csc10
Term
What is the angle of depression? What is the angle of elevation?
Definition
[image]
Term
What is the Law of sines
Definition
[image]
Term
What kind of triangle can you use the law of sines with?
Definition
AAS, ASA, SSA
Term
What triangles can you use the law of cosines with?
Definition
SAS, SSS
Term

What is the law of cosines?

(for the side, and for the angle)

Definition
[image]
Term

Acute SSA Triangle

OPP<HT  how many triangles?

Definition
0 triangles when OPP<HT
Term

Acute SSA Triangle

OPP=HT How many triangles?

Definition
1 Triangle when OPP=HT
Term

Acute SSA Triangle

HT<OPP<ADJ how many triangles?

Definition
2 triangles when Ht<OPP<ADJ
Term

Acute SSA Triangle 

OPP >= ADJ how many triangles ?

Definition
1 triangle when OPP>= ADJ
Term

Obtuse SSA Triangle

OPP<=ADJ how many triangles?

Definition
0 triangles if OPP<=ADJ
Term

Obtuse SSA triangle

OPP>Adj How many triangles?

Definition
1 triangle when OPP>adj
Term

List cases where SSA triangles make 0 triangles

acute:

obtuse:

 

Definition

Acute:

OPP<HT

Obtuse:

OPP<=ADJ

Term

List Cases where SSA triangles make 1 triangle

Acute:

Obtuse:

Definition

Acute:

OPP=HT

OPP>=ADJ

Obtuse:

OPP>ADJ

Term

List Cases when ssa triangles make 2 triangles

Acute:

Obtuse:

 

Definition

Acute: 

Ht<OPP<Adj

Obtuse:

no cases

Term
List formulas needed for an SAS triangle to find Area
Definition

A=1/2 abSinC

=1/2 acSinB

=1/2bcSinA

Term
List formulas needed for an SSS triangle to find area
Definition

s=1/2 (a+b+c)

A=sqrt(s(s-a)(s-b)(s-c))

Term

Given: triangle A=19 a=25 c=30 Find C

 

List the steps to solve this problem:

Definition

1. (optional) draw the triangle and determine what kind of triangle it is (SSA)

2. Solve for height using SOHCAHTOA

3. Determine how many triangles you have using the height (2)

4.use the law of sines to find C1

5. subtract C1 from 180 to find C2

Term

Given: Triangle B=34, b=3, a=4 c?

 

List the steps to solve this problem:

Definition

1. (Optional) Draw the triangle and determine the type of triangle (SSA)

2. Calculate height using SOHCAHTOA to determine the number of triangles (2)

3. Use the law of sines to solve angle A

4. Subtract angle A and Angle B from 180 to find Angle C

5. Use the law of sines to find c1

6. Subtract angle A from 180 to find the new angle A

7. Subtract the new angle A and Angle B from 180 to find angle C

8. Use the law of sines to find c2

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