Download Jan. 4 1. Find the third angle of a right triangle if one acute angle is

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Think back to geometry. What are some
ways to prove triangles are congruent?
1. Find the third angle of a right triangle if
one acute angle is 25 degrees.
2. Find x.
x
18
36
x
6.1 Law of Sines
Oblique Triangle - a triangle that is not a
right triangle.
b
h
A
Right triangle trigonometry does not apply
to oblique triangle
(no SOHCAHTOA, no Pythagorean
Theorem.)
Solve the triangle means to find the measure
of all angles and the lengths of all side.
sin A=
C
sin B=
a
B
c
C
sin A=
h
a
b
A
c
B
sin B=
Solve the Triangle
A
c
a
Law of Sines
B
c
a
A
C
b
or
Remember to check that the longest side is opposite the largest angle and the shortest side is opposite the smallest angle.
Solve the Triangle
If you know three pieces of information including an angle and the length of the opposite side, you can use the Law of Sines to find the other 3 pieces of information.
A
a
B
The Ambiguous Case
If we are given two sides and an angle opposite one of the two sides (SSA), the given information may result in one triangle, two triangles, or no triangle at all. SSA is known as the ambiguous case when using the Law of Sines because the given information may result in one triangle, two triangles, or no triangle at all.
Assume the angle given is acute.
Determine the number of triangles possible.
A = 62, a = 5, b = 15
A = 31, a = 22, b = 9
C
C
a
C
b
b
h
A
c
B
A
h
b
a
c
a
A
a < h < b, no triangle
a > b one triangle
h
a
A = 99, a = 9.2, b = 5.5
B
B
h < a < b
Two triangles
A =25, a = 11, b = 14
Note: Angle A is obtuse will either produce no triangle if a < b or one triangle if a > b.
Check for ambiguous case if:
1. Given angle is acute
2. Side opposite given angle is the smaller of the two sides.
A = 125, a = 16, b = 30
Solve triangle ABC if A = 35°, a = 12, and b = 16.
Mathlab 6.1 Day 1
Quiz 6.1/6.2 Friday