Download Solving Triangles

Pre Calculus
8.2/8.3 Warm Up
The Law of Sines & Cosines
Find the missing segment lengths and angles of the triangles.
1.
B
a
106.2
61.7º
C
2.
b
A
d
F
E
23
13
D
Pre Calculus
8.2/8.3 NOTES
The Law of Sines & Cosines
OBJECTIVES:
To use the law of sines and cosines to find unknown parts of a
triangle.
Solving oblique triangles
Oblique triangle:
The law of sines
The Law of Sines
In any triangle ABC,
The sides are proportional to the sines of the opposite
angles
Solving Triangles (AAS and ASA)
1. In ∆EFG, e = 4.56, < E = 43º, and < G = 57º. Solve the triangle.
2. During a rescue mission, a Marine fighter pilot receives data on an
unidentified aircraft from an AWACS plane and is instructed to
intercept the aircraft. The diagram below appears on the screen,
but before the distance to the point of interception appears on the
screen, communications are jammed. Fortunately, the pilot
remembers the law of sines. How far must the pilot fly?
Z
115º
X 500km 27º
(unidentified
aircraft)
Y (pilot)
Solving tiangles (SSA)
3. In ∆QRS, q = 15, r = 28 and Q = 43.6º. Solve the triangle.
4. In ∆XYZ, x = 23.5, y = 9.8, and X = 39.7º. Solve the triangle.
The Law of Cosines
The Law of Cosines
In any triangle ABC,
The square of a side is the sum of the squares of the other
two sides, minus twice the product of those sides and the
cosine of the included angle.
Solving Triangles (SAS)
5. Solve ∆ABC if a = 32, c = 48, and B = 125.2º.
Solving Triangles (SSS)
6. Solve ∆RST if r = 3.5, s = 4.7, and t = 2.8.
8. In ∆ABC, three measures are given. Determine which law to use
when solving the triangle.
a) a = 14, b = 23, c = 10
b) a = 207, B = 43.8º, C = 57.6º
c) A = 112º, C = 37º, a = 84.7
d) B = 101º, a = 960, c = 1042
e) b = 17.26, a = 27.29, A = 39º
f) A = 61º, B = 39º, C = 80º