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Transcript
 Step
1: Draw a triangle
 Step 2: Label your smallest angle A
 Step 3: Label your medium angle B
 Step 4: Label your largest angle C
 Step 5: Label your side opposite angle A, a
 Step 6: Label your side opposite angle B, b
 Step 7: Label your side opposite angle C, c
 What
do you recall from Geometry about the
sides opposite the angles?
 What
makes a triangle oblique?
 How is trigonometry useful to solve and find
the areas of oblique triangles?
 What situations create the ambiguous case
for the Law of Sines?
 What is a directional bearing and how is it
applied to real life situations?
 How do you use trigonometric functions to
solve real life problems?
The student will be able to understand and
apply solving real world applications using laws
of sine and cosine for oblique triangles.
 Do
Now
 Law of Sines
 Break
 Practice
 Closure
 Homework
𝑏
𝑐
𝑎
=
=
𝑆𝑆𝑆 𝐴 𝑆𝑆𝑆 𝐵 𝑆𝑆𝑆 𝐶
 What


does it mean?
Calculate the measure of ALL the angles
Calculate the measure of ALL the sides
 What

Any triangle that does not have a right angle
 How

are they?
do you solve them?
You need to know the measure of at least one
side and the measure of any two other parts.




AAS or ASA – Law of Sines
SSA – Law of Sines
SSS – Law of Cosines
SAS – Law of Cosines
 Why
is this important?
 Because
of prevailing winds, a tree grew so
that it was leaning 6° from the vertical
(90°). At a point 30 meters from the tree,
the angle of elevation to the top of the tree
is 22.5°. Find the height of the tree.
 SSA



No such triangle exists
One triangle exists
Two distinct triangles exists
How can you minimize mistakes?
Draw a picture!
 Solve



the given triangle(s)
A = 60°
a=4
b = 14
 Solve



the given triangle(s)
A = 58°
a = 4.5
b=5
 The
area of ANY triangle is one-half the
product of the length of two sides times the
sine of their included angle:
 𝐴𝐴𝐴𝐴
=
 𝐴𝐴𝐴𝐴
=
 𝐴𝐴𝐴𝐴
=
1
𝑏𝑏 𝑆𝑆𝑆 𝐴
2
1
𝑎𝑐 𝑆𝑆𝑆 𝐵
2
1
𝑎𝑏 𝑆𝑆𝑆 𝐶
2
 Find
the area of a triangular lot with side
lengths that measure 24 yards and 18 yards
and form an 80° angle.
 On
a small lake, a child swam from point A to
point B at a bearing of N 28°E. The child
then swam to point C at a bearing of N 58°W.
Point C is 800 meters due north of point A.
How many total meters did the child swim?
 How
do you use trigonometry to solve and
find the areas of oblique triangles?
 Textbook
pages 414-415 #11-23 ODD, 25, 26