Download Trig HW - mvhs

SANTA CLARA COUNTY OFFICE OF EDUCATION
North County Regional Occupational Program (NCROP)
Engineering Technology
Trigonometry Tutorial & Problems
c
Θ2
a
Θ1
b
Characteristics of the Right Triangle
One of the three angles is 90º
The sum of the three angles is 180º. (θ1º+θ2º+90º = 180º)
The two sides are length a and b
The long side, or hypotenuse, is length c
Pythagorean's Theorem: In a right triangle whose legs have length a and b, and whose
hypotenuse has length c, then c2 = a2 + b2.
Example 1: If side a = 5 inches and side b = 10 inches, what is the length of hypotenuse c?
Pythagorean's Theorem states c2 = a2 + b2
c2 = (5 inches)2 + (10 inches)2
c2 = 25 inches2 + 100 inches2
c2 = 125 inches2
c = √(125 inches2)
This is an acceptable answer
c = √(5*5*5 inches2)
c = 5√5 inches
This is a better answer
c = 11.18
Use a calculator for the best answer
Example 2: If side a = 6 inches and hypotenuse c = 12 inches, what is the length of side b?
Pythagorean's Theorem states c2 = a2 + b2
c2 – a2 = b2
(12 inches)2 – (6 inches)2 = b2
144 inches2 – 36 inches2 = b2
108 inches2 = b2
√(108 inches2) = b
This is an acceptable answer
2
√(2*2*3*3*3 inches ) = b
6√3 inches = b
This is a better answer
10.39 = b
Use a calculator for the best answer
SANTA CLARA COUNTY OFFICE OF EDUCATION
North County Regional Occupational Program (NCROP)
Engineering Technology
c = 5 inches
Θ2
a = 3 inches
Θ1
b = 4 inches
Sine (abbreviated 'sin'): In a right triangle, sin of an angle θ is the length of the opposite
side divided by the length of the hypotenuse.
Example: If side a = 3 inches, side b = 4 inches, and side c = 5 inches, what is sinθ1 and
sinθ2?
sinθ1 = (side a / hypotenuse c)
sinθ1 = (3 inches / 5 inches)
sinθ1 = 0.60
sinθ2 = (side b / hypotenuse c)
sinθ2 = (4 inches / 5 inches)
sinθ2 = 0.80
Cosine (abbreviated 'cos'): In a right triangle, cos of an angle θ is the length of the
adjacent side divided by the length of the hypotenuse.
cosθ1 = (side b / hypotenuse c)
cosθ1 = (4 inches / 5 inches)
cosθ1 = 0.80
cosθ2 = (side b / hypotenuse c)
cosθ2 = (3 inches / 5 inches)
cosθ2 = 0.60
A common way to memorize these relationships is the term, ‘SOHCAHTOA’
‘SOH” represents ‘Sine is Opposite over Hypotenuse’
‘CAH’ represents ‘Cosine is Adjacent over Hypotenuse’
‘TOA’ represents ‘Tangent is Opposite over Adjacent’
SANTA CLARA COUNTY OFFICE OF EDUCATION
North County Regional Occupational Program (NCROP)
Engineering Technology
c
a
b
Given the right triangle above and the following lengths, calculate the length of the missing
side. (Hint: Don't forget the units)
Problem
1
2
3
4
5
6
7
8
9
10
Length of Side a
3 meters
5 yards
1 inch
8 miles
5 feet
8 inches
1 mm
Length of Side b
4 meters
8 yards
1 inch
4 miles
1 foot
8 mm
2 yards
Length of Hypotenuse c
3 feet
15 mm
3 yards
13 feet
16 inches
3 mm
SANTA CLARA COUNTY OFFICE OF EDUCATION
North County Regional Occupational Program (NCROP)
Engineering Technology
c
Θ2
a
Θ1
b
Given the right triangle above, calculate the sin and cos given the following edge lengths.
The first one is done as an example.
#
Ex
Length a
4 miles
Length b
6 miles
Hypotenuse c
2√13 miles
5 feet
Problem a)
sinθ1= _________
sinθ1 = a/c
=(4 miles) / (2√13
miles)
=2/√13
sinθ1=
Problem b)
cosθ1= __________
cosθ1 = b/c
=(6 miles) / (2√13
miles)
=3/√13
sinθ2=
1
3 feet
4 feet
2
5 meters
12 meters
13 meters
cosθ1=
sinθ1=
3
6 inches
4 inches
2√13 inches
cosθ1=
cosθ2=
4
1 mm
3√7 mm
8 mm
sinθ2=
cosθ2=
5
2√21 cm
4 cm
10 cm
sinθ1=
cosθ2=