Download Unit 7b

Unit 7b
Right Triangles and Trigonometry
By: Shiven Acharya and
Danielle Kevelin
Key Concepts
SOH CAH TOA
Sine
Cosine
Tangent
SOH: sin(A)=Opp/Hyp
CAH: cos(A)=Adj/Hyp
TOA: tan(A)=Opp/Adj
If tan A = x, then tan⁻¹ x =
m∠A
Inverse Sine
m∠A
If ABC has side lengths
a, b, and c then sin A = sin B = sin C
a
b
c
**you cannot use sine for obtuse ∠s**
B
c
a
A
Hypotenuse
Opposite
Law of Sine & Cosine
Law of Sines : you need 1 ∠ & opp side
Inverse Tangent
If sin A = y, then sin⁻¹ y =
A
Adjacent
Inverse Trig
Inverse Cosine
If cos A = z, then cos⁻¹ z =
m∠A
B
C
C
b
A
Law of Cosines : If
ABC has side
lengths a, b, and c then
a² = b² + c² - 2bc cos A
b² = a² + c² - 2ac cos B
c² = a² + b² - 2ab cosC
Common Mistakes
1.
A common mistake while using SOHCAHTOA is mixing up the sides. For example, you might
put in Sine when you only have the adjacent and hypotenuse values. Some suggestions to stop
this mistake from repeating are to check your work using SOHCAHTOA and maybe use Trig.
inverses. You should also try to understand SOHCAHTOA better so you won’t make that mistake
again.
1.
Another common mistake is using an adjacent side instead of using the opposite side.
An easy solution to this problem is to use SOHCAHTOA a bit more to familiarize yourself with it.
1.
Someone may also, while doing a problem with inverse trig., may forget to use sin inverse on
the calculator. Almost all of these mistakes are silly mistakes and can be stopped by practicing
over and over again.
2. Another mistake could be using law of sin for an obtuse angle.
Connections
● Unit 5, the similarity unit in which we used angles and sides to prove
triangles congruent.
o
If you had a problem like in unit 5 but didn’t have enough information to prove the triangle
congruent, you could use trig.
● Unit 11
o
o
You could use trig to find unknown measurements
Helpful in surface area when you don’t have enough information.
● Unit 10: Measuring Length and Area
○ Trig was helpful in this unit when you only had one angle and side measurement.
Examples
Find sin (S)
sin(S)=
S
opp/hyp=
This one
is easy!
63
T
RT/SR=
65
16/65= S
16
R
S≈ 0.246153846
Examples
Find x.
sin(21)= opp/hyp
= 1200/x
21
x*sin(21)=1200
x
1200
x= 1200/sin(21)
x≈ 1200/0.3584
x≈ 3348.2
This one’s
harder!
Examples
c
a
Let A be any acute angle
of a right triangle. Show
that tan(A)=
sin(A)/cos(A).
Sin(A)= a/c
Cos(A)= b/c
b
A
Sin(A)/Cos(A)=
a/c x c/b=
a/b=
Tan(A)
This one’s
hard!
Real Life Situation
x
You are trying to decorate the gym for an end of the
year party. You need to know how tall and how long the bleachers
y
are so you can cut the right sized ribbon.Find all sides of
the triangle. Round to the nearest yard.
38°
6 yd
cos(38)=adjacent
hypotenuse
cos(38) = 6
y
y * cos (38) = 6 * y
y
y=6
y=7.61
cos(38)
You can use Pythagorean
theorem to solve for x.
y≈8
a²+b²=c²
x²+6²=8²
x²=64-36
x²=28
x=2√7
x=2√7
You can use SOHCAHTOA to
solve for x.
tan(38)=opposite
adjacent
tan(38)= x
6
6 * tan(38)=x
x=4.69
x≈5