 134.1: Find the area of ABC to the nearest tenth.
 134.2: Find the area of ABC to the nearest tenth.
 134.3: C A B 70 80
 134.4: C A B 75 25 14
 134.5: B 20 140 38
 134.6: A = 123, a = 12, b = 23
 134.7: A = 30, a = 3, b = 4
 134.8: A = 55, a = 10, b = 5
 134.9: A = 145, a = 18, b = 10
 134.10: WOODWORKING Latisha is to join a 6meter beam to a 7meter beam so ...
 134.11: C B 127 9 m
 134.12: B A C 44 7 yd 8 yd
 134.13: B = 85, c = 23 ft, a = 50 ft
 134.14: A = 60, b = 12 cm, c = 12 cm
 134.15: C = 136, a = 3 m, b = 4 m
 134.16: B = 32, a = 11 mi, c = 5 mi
 134.17: C B A 17 62
 134.18: A B 48 59 62
 134.19: C B 122 22 31
 134.20: B 4 A 65
 134.21: B C 16 A 20 63
 134.22: B A 2 3 75
 134.23: A = 124, a = 1, b = 2 n
 134.24: A = 99, a = 2.5, b = 1.5
 134.25: A = 33, a = 2, b = 3.5
 134.26: A = 68, a = 3, b = 5
 134.27: A = 30, a = 14, b = 28
 134.28: A = 61, a = 23, b = 8
 134.29: A = 52, a = 190, b = 200
 134.30: A = 80, a = 9, b = 9.1
 134.31: RADIO A radio station providing local tourist information has its t...
 134.32: FORESTRY Two forest rangers, 12 miles from each other on a straight...
 134.33: A = 50, a = 2.5, c = 3
 134.34: B = 18, C = 142, b = 20
 134.35: BALLOONING As a hotair balloon crosses over a straight portion of ...
 134.36: OPEN ENDED Give an example of a triangle that has two solutions by ...
 134.37: FIND THE ERROR Dulce and Gabe are finding the area of ABC for A = 6...
 134.38: REASONING Determine whether the following statement is sometimes, a...
 134.39: Writing in Math Use the information on page 785 to explain how trig...
 134.40: ACT/SAT Which of the following is the perimeter of the triangle sho...
 134.41: REVIEW The longest side of a triangle is 67 inches. Two angles have...
 134.42: cos 30
 134.43: cot (_ 3 )
 134.44: csc (_ 4 )
 134.45: 300
 134.46: 47
 134.47: 5 3
 134.48: AERONAUTICS A rocket rises 20 feet in the first second, 60 feet in ...
 134.49: a2 = 32 52 2(3)(5) cos 85
 134.50: c2 = 122 102 2(12)(10) cos 40
 134.51: 72 = 112 92 2(11)(9) cos B 5
 134.52: 132 = 82 62 2(8)(6) cos A
Solutions for Chapter 134: Law of Sines
Full solutions for Algebra 2, Student Edition (MERRILL ALGEBRA 2)  1st Edition
ISBN: 9780078738302
Solutions for Chapter 134: Law of Sines
Get Full SolutionsChapter 134: Law of Sines includes 52 full stepbystep solutions. Algebra 2, Student Edition (MERRILL ALGEBRA 2) was written by and is associated to the ISBN: 9780078738302. This textbook survival guide was created for the textbook: Algebra 2, Student Edition (MERRILL ALGEBRA 2), edition: 1. Since 52 problems in chapter 134: Law of Sines have been answered, more than 60747 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

Diagonalizable matrix A.
Must have n independent eigenvectors (in the columns of S; automatic with n different eigenvalues). Then SI AS = A = eigenvalue matrix.

Free variable Xi.
Column i has no pivot in elimination. We can give the n  r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

Iterative method.
A sequence of steps intended to approach the desired solution.

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

Matrix multiplication AB.
The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

Outer product uv T
= column times row = rank one matrix.

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.