Law of Sines Solving Angle
Side Angle
This week we are showing you how to
find the missing angle and sides of a triangle when you have two angles and a
side. This method is used to find
distance.
Teaser:
Raspune has an enemy ship in his sights and is finding its exact distance. Two sensors on his ship are arranged on a baseline
of 30 meters (g). One sensor
finds and angle of 50 degrees (a) and the other registers 44 degrees (b). Find the missing parts of the triangle and
average a and b to find the correct distance.
sin
a/a = sin b/b = sin g/c
The
ratio of the sine of an angle to its opposite side is the same as the ratio of
the sine of either of the other angles to its opposite side.
Example : If b = 43o, g = 36o, and a = 90 cm, find a, b, and c.
a + b + g = 180o
The
sum of the angles of a given triangle is 180o.
a + 43o + 36o = 180o
b = 43o
and g = 36o
a + 79o = 180o
Add
43 and 36
a + 79o – 79o = 180o
– 79o
Subtract
79 from both sides of the equation.
a = 101o
Subtract
79 from a and Subtract 79
from 180
sin a/a = sin /b
Law
of sines
sin 101o/90
cm = sin 43o/ b
b = 43o, a = 90 cm and a = 101o
90b cm(sin 101o/90
cm) = 90b cm(sin 43o/ b)
Multiply both side
of the equation by 90b cm
b(sin 101o)
= 90 cm(sin 43o)
90b cm times sin
101o/90 cm and 90b cm times sin 43o
(b(sin 101o))/
(sin 101o) = (90 cm(sin 43o))/ (sin 101o)
Divide both sides
of equation by sin 101o
b = (90
cm(sin 43o))/ (sin 101o)
Divide b(sin 101o)
by sin 101o and 90 cm(sin 43o) by sin 101o
b = (90 cm
(.6820))/.9816
sin 43o
= .6820 and sin 101o = .9816
b = 62.5
cm
Perform indicated
operations
sin a/a = sin g/c
Law
of sines
sin 101o/90
cm = sin 36o/ c
g = 36o, a = 90 cm and a = 101o
90c cm(sin 101o/90
cm) = 90c cm(sin 36o/ c)
Multiply both side
of the equation by 90b cm
c(sin 101o)
= 90 cm(sin 36o)
90c cm times sin
101o/90 cm and 90c cm times sin 36o
(c(sin 101o))/
(sin 101o) = (90 cm(sin 36o))/ (sin 101o)
Divide both sides
of equation by sin 101o
c = (90
cm(sin 36o))/ (sin 101o)
Divide c(sin 101o)
by sin 101o and 90 cm(sin 36o) by sin 101o
c = (90 cm
(.5878))/.9816
sin 43o
= .5878 and sin 101o = .9816
c = 53.9
cm
Perform indicated
operations
Problems
1) If b = 27.5o, g = 54.5o, and a = 9.27 mm, find a, b, and c.
2) If b = 12.67o, g = 100o, and a = 17.3 km, find a, b, and c.