Download Law of Cosines Law of Sines

Trigonometric Ratios Review
(and some other stuff too!)
2) Right Triangle Trig Ratios:
Special Right Triangles
1)
45-45-90
30-60-90
Feb 16­8:05 PM
Feb 1­2:20 PM
Law of Cosines
Law of Sines
A
c
A
Used for SSS, SAS
b
c
B
C
a
Used for AAS, ASA, SSA
b
B
C
a
Feb 1­3:15 PM
Feb 1­3:18 PM
1
Law of Sines...
The Ambiguous Case
The SSA situation (two sides and an angle opposite one of the two sides) is called the ambiguous case because there may be no triangle, one triangle or two triangles satisfying the given conditions.
Example: No Triangle
o
b = 50, a = 33, A = 132
Example: Two Triangles
o
a = 125, A = 25 , b = 150
Feb 1­3:24 PM
Example 2:
From a point 65 feet in front of a church, the angles of elevation to the base of the steeple and the top of the steeple are 35o and 43o respectively.
Find the height of the steeple.
Example 1:
A ladder 16 feet long leans against the side of a house. Find the height h from the top of the ladder to the ground if the angle of elevation of the ladder is 74o.
Feb 1­3:22 PM
Example 3:
From the time a small airplane is 100 feet high and 1600 ground feet from its landing runway, the plane descends in a straight line to the runway. Determine the plane's angle of decent.
100 ft.
1600 ft.
Feb 1­3:23 PM
Feb 1­3:23 PM
2
Two airplanes, at points A and B as shown in the diagram below, have elevations of
23,000 ft. and 18,000 ft. respectively.
Both are flying east toward an airport control tower at T.
From T, the angle of elevation of the airplane at A is 4o, and the angle of elevation of the
airplane at B is 2.5o. How far apart (in mi) are the airplanes?
Pg. 493 # 1 ­ Law of Sines and Cosines Problem.
Mi
ft
4.7 X
O
4o
2.5o
Feb 1­3:27 PM
25o
T
α
Q
r
rro
α
Blue Mirror
6 ft
23,000 ft.
18,000 ft.
P
θ
θ
Red
T
Aug 16­12:38 PM
3
Attachments
ambiguous case.gsp