Download Law of Sines

7 Days
Two days

In any triangle, the ratio of the sine of any
angle to the side opposite that angle is equal
to the ratio of the sine of another angle to the
side opposite that angle.
sin A sin B sin C


a
b
c
A
c
b
C
B
a

The Law of Sines can be used anytime that we
are given the following information about a
triangle:
◦ 1. Two sides and an angle opposite one of them
(SSA)
◦ 2. Two angles and any side (AAS or ASA)

If we have either SAS or SSS the Law of Sines
will not be sufficient. (to be continued…)

Find the missing pieces of the triangle given:
C  120, B  45, c  20
A
c
b
C
B
a

Find the missing pieces of the triangle given:
B  82, b  50, c  115
A
c
b
C
B
a

Find the missing pieces of the triangle given:
B  82, b  50, c  115
??
50
??
82*
115


If we are given two angles and any side, the
Law of Sines results in exactly one triangle.
However, if we are given two sides and an
angle opposite one of the those sides, we
could get one triangle, two triangles, or no
triangles.

Find the missing pieces of the triangle given:
  5320' , a  140, c  115
A
c
b
C
B
a

A surveyor is trying to determine the distance
between A and B and chooses a point C that
is 375yds from A and 530yds from B. If
<BAC has a measure of 4930' , what is the
distance between A and B?

p527 #1,2,4,5,14,17 - 19,21
Four Days


Solve A  15, c  18, b  20 using the Law of
Sines.
Can we solve a  20, b  15, c  18 with the
Law of Sines?

We need the Law of Cosines to solve triangles
that are SAS or SSS.
The Law of Cosines :
a 2  b 2  c 2  2bc cos A
a2  b2  c2
cos A 
 2bc

SAS - C  48, a  18, b  15

SSS – a  25, b  19, c  36
 Note: Find the largest angle first since arccos can give
obtuse angles!

p536 #1,3,4,6,9,11,13 - 15

A reconnaissance airplane P, flying at 10,000ft
above point R on the surface of the water, spots
a submarine S at an angle of depression of 37*
and a tanker T at an angle of depression of 21*,
as shown in the diagram. If <SPT is 110*, what
is the distance between the tanker and the
submarine.



p528 #24
p537 #12
p580 #41,43,45,47
One Day


We can find the area of a triangle given the
lengths of all three sides or two sides and an
angle.
If we only know the lengths of sides we will
use Heron’s Formula:
Area  s ( s  a )( s  b)( s  c)
abc
where s 
;
2
1
2
the perimeter

Find the area of the triangle if
a=47, b=58, and c=78

Find the area of a triangle given A=100*,
b=16, and c=18.
h
 sin 100
18
h  18sin 100
a=
h=_____
A  12 bh
c=18
A  12 (16)(18 sin 100)
=100
=100
b=16
A  141.8

p537 #18,22,29,31,33,35

5-8 paper Glencoe area of triangle

7.1 & 7.2 review paper