 2.5.1: When bearing is given as a single angle measure, how is the angle r...
 2.5.2: When bearing is given as N (or S), then an acute angle measure, and...
 2.5.3: Why is it important to draw a sketch before solving trigonometric p...
 2.5.4: How should the angle of elevation (or depression) from a point X to...
 2.5.5: Concept Check An observer for a radar station is located at the ori...
 2.5.6: Concept Check An observer for a radar station is located at the ori...
 2.5.7: Concept Check An observer for a radar station is located at the ori...
 2.5.8: Concept Check An observer for a radar station is located at the ori...
 2.5.9: Concept Check An observer for a radar station is located at the ori...
 2.5.10: Concept Check An observer for a radar station is located at the ori...
 2.5.11: Concept Check An observer for a radar station is located at the ori...
 2.5.12: Concept Check An observer for a radar station is located at the ori...
 2.5.13: The ray y = x, x 0, contains the origin and all points in the coord...
 2.5.14: Repeat Exercise 13 for a bearing of 150.
 2.5.15: Distance Flown by a Plane A plane flies 1.3 hr at 110 mph on a bear...
 2.5.16: Distance Traveled by a Ship A ship travels 55 km on a bearing of 27...
 2.5.17: Distance between Two Ships Two ships leave a port at the same time....
 2.5.18: Distance between Two Ships Two ships leave a port at the same time....
 2.5.19: Distance between Two Docks Two docks are located on an eastwest li...
 2.5.20: Distance between Two Lighthouses Two lighthouses are located on a n...
 2.5.21: Distance between Two Ships A ship leaves its home port and sails on...
 2.5.22: Distance between Transmitters Radio direction finders are set up at...
 2.5.23: Flying Distance The bearing from A to C is S 52 E. The bearing from...
 2.5.24: Flying Distance The bearing from A to C is N 64 W. The bearing from...
 2.5.25: Distance between Two Cities The bearing from WinstonSalem, North C...
 2.5.26: Distance between Two Cities The bearing from Atlanta to Macon is S ...
 2.5.27: Solve the equation ax = b + cx for x in terms of a, b, and c. (Note...
 2.5.28: Explain why the line y = 1tan u21x  a2 passes through the point 1a...
 2.5.29: Find the equation of the line passing through the point 125 , 02 th...
 2.5.30: Find the equation of the line passing through the point 15 , 02 tha...
 2.5.31: Find h as indicated in the figure.
 2.5.32: Find h as indicated in the figure.
 2.5.33: Height of a Pyramid The angle of elevation from a point on the grou...
 2.5.34: Distance between a Whale and a Lighthouse Debbie GlocknerFerrari, ...
 2.5.35: Height of an Antenna A scanner antenna is on top of the center of a...
 2.5.36: Height of Mt. Whitney The angle of elevation from Lone Pine to the ...
 2.5.37: (Modeling) Distance between Two Points Refer to Example 3. A variat...
 2.5.38: Height of a Plane above Earth Find the minimum height h above the s...
 2.5.39: Distance of a Plant from a Fence In one area, the lowest angle of e...
 2.5.40: Distance through a Tunnel A tunnel is to be built from A to B. Both...
 2.5.41: (Modeling) Highway Curves A basic highway curve connecting two stra...
 2.5.42: Length of a Side of a Piece of Land A piece of land has the shape s...
 2.5.43: (Modeling) Stopping Distance on a Curve Refer to Exercise 41. When ...
 2.5.44: (Modeling) Distance of a Shot Put A shotputter trying to improve p...
Solutions for Chapter 2.5: Further Applications of Right Triangles
Full solutions for Trigonometry  10th Edition
ISBN: 9780321671776
Solutions for Chapter 2.5: Further Applications of Right Triangles
Get Full SolutionsSince 44 problems in chapter 2.5: Further Applications of Right Triangles have been answered, more than 18047 students have viewed full stepbystep solutions from this chapter. Trigonometry was written by and is associated to the ISBN: 9780321671776. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 2.5: Further Applications of Right Triangles includes 44 full stepbystep solutions. This textbook survival guide was created for the textbook: Trigonometry, edition: 10.

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

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

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

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 .

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

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.

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).

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(D» O.

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

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

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.