Transcript Ch 6 – Additional Topics in Trigonometry

Ch 5.8 – The Law of Cosines
Can you solve the triangle?
YES, but WHY?
A
15
C
9
40o B
Can you solve the triangle?
YES, but WHY?
A
4
B
36o
10
C
Can you solve the triangle?
Not yet – why?
A
8
B
14
19
C
LAW of COSINES
a2 + b2 – 2abcosC = c2
You can use the Law of Cosines
when you have:
 all 3 sides
 2 sides & their included angle
Now you can solve this triangle!
A
8
B
14
19
C
Try solving this triangle!
A
65
B
40o
30
C
Triangulation
the process of determining the location of a point by measuring
angles to it from known points at either end of a fixed
baseline, rather than measuring distances to the point
directly. The point can then be fixed as the third point of a
triangle with one known side and two known angles.
Examples: finding the height of a cliff, the distance a ship is
from shore, the position of a space craft, surveying land…
Surveyor
A bridge is going to be built across a river. A surveyor is sent out to
find the distance across the river. He sets up two markers on one
side of the river, 150 m apart, and a third marker on the other side.
He then measures the angles from his two markers to the third.
One angle measures 52o and the other is 82o. Find the width of the
river.
Area of a
Triangle
Height & Base
½bh
2 sides &
Included Angle
3 Angles &
1 Side
All 3 Sides
½ absinC
½ a2 sinB sinC
sinA
Heron’s Formula
where s = ½(a + b + c)
Kidnapping
A call came in to 911 from a lady that said she was kidnapped.
She had to hang up her phone before she could tell the
operator where she was. The police traced the call to one of 3
cell towers. How big is the area they have to search?
11 mi
5 mi
7 mi