Download Lecture notes for Section 4.4

Tech Math 2 Notes
Section 4.4
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Review Topics:
Angle Precision
1
0.1 or 10
0.01 or 1
Angles and Accuracy of Trig Functions
Trig Function Accuracy
Example
2 sig. figs.
sin17  0.29 , tan85  11
3 sig. figs.
sin1.1  0.0192 ,
cos520'  0.996
4 sig. figs.
cos 45.00  0.7071 ,
tan8013'  5.799
Calculating Other Trig Functions
Definition
Example
cos 
1
1
cot  

cot 82.3 
 0.135
sin  tan 
tan 82.3
1
1
sec  
sec 22 
 1.1
cos 
cos 22
1
1
csc  
csc 72.67 
 1.048
sin 
sin 72.67
Section 4-4: The Right Triangle
SOH CAH TOA:
opp b

hyp c
opp b
tan  

adj a
1
hyp c
sec 


cos adj a
sin  
adj a

hyp c
1
adj a
cot  


tan  opp b
1
hyp c
csc 


sin  opp b
cos  
In solving a triangle, you are given three parts of a triangle (one of which must be the length of a side), and
then are expected to calculate the other three parts.
Tech Math 2 Notes
Section 4.4
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The sum of the angles of a triangle is 180, so for a right triangle (one angle 90), the two acute angles add up to
the remaining 90 (mathematical lingo: they are complementary).
To solve a right triangle:
1. Make a sketch of the triangle, label sides and angles consistently (a, b, and c for the legs and
hypotenuse; A and B for the complementary angles), and label the given information.
2. Find a way to relate the unknown parts to the given information using a trig function (sine, cosine, or
tangent) or the Pythagorean Theorem (a2 + b2 = c2). Try to use original given information to minimize
rounding errors.
3. Check your work:
a. Make sure the sides obey the Pythagorean Theorem.
b. Make sure the angles add up to 180.
c. Make sure unused trig functions give the right answers.
d. Make sure that the longest side is opposite the largest angle, and the shortest side is opposite the
smallest angle.
Practice:
1. Solve a right triangle given two legs:
2. Solve a right triangle given a leg and a hypotenuse:
Tech Math 2 Notes
Section 4.4
3. Solve a right triangle given an angle and an adjacent side:
4. Solve a right triangle given an angle and an opposite side:
5. Solve a right triangle given an angle and the hypotenuse:
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