 2.4.1: Match each equation in Column I with the appropriate right triangle...
 2.4.2: Match each equation in Column I with the appropriate right triangle...
 2.4.3: Match each equation in Column I with the appropriate right triangle...
 2.4.4: Match each equation in Column I with the appropriate right triangle...
 2.4.5: Match each equation in Column I with the appropriate right triangle...
 2.4.6: Match each equation in Column I with the appropriate right triangle...
 2.4.7: Concept Check Refer to the discussion of accuracy and significant d...
 2.4.8: Concept Check Refer to the discussion of accuracy and significant d...
 2.4.9: Concept Check Refer to the discussion of accuracy and significant d...
 2.4.10: Concept Check Refer to the discussion of accuracy and significant d...
 2.4.11: Concept Check Refer to the discussion of accuracy and significant d...
 2.4.12: Concept Check Refer to the discussion of accuracy and significant d...
 2.4.13: Solve each right triangle. When two sides are given, give angles in...
 2.4.14: Solve each right triangle. When two sides are given, give angles in...
 2.4.15: Solve each right triangle. When two sides are given, give angles in...
 2.4.16: Solve each right triangle. When two sides are given, give angles in...
 2.4.17: Solve each right triangle. When two sides are given, give angles in...
 2.4.18: Solve each right triangle. When two sides are given, give angles in...
 2.4.19: Solve each right triangle. When two sides are given, give angles in...
 2.4.20: Solve each right triangle. When two sides are given, give angles in...
 2.4.21: Concept Check Answer each question. Can a right triangle be solved ...
 2.4.22: Concept Check Answer each question. If we are given an acute angle ...
 2.4.23: Concept Check Answer each question. Why can we always solve a right...
 2.4.24: Concept Check Answer each question. Why can we always solve a right...
 2.4.25: Solve each right triangle. In each case, C = 90. If angle informati...
 2.4.26: Solve each right triangle. In each case, C = 90. If angle informati...
 2.4.27: Solve each right triangle. In each case, C = 90. If angle informati...
 2.4.28: Solve each right triangle. In each case, C = 90. If angle informati...
 2.4.29: Solve each right triangle. In each case, C = 90. If angle informati...
 2.4.30: Solve each right triangle. In each case, C = 90. If angle informati...
 2.4.31: Solve each right triangle. In each case, C = 90. If angle informati...
 2.4.32: Solve each right triangle. In each case, C = 90. If angle informati...
 2.4.33: Solve each right triangle. In each case, C = 90. If angle informati...
 2.4.34: Solve each right triangle. In each case, C = 90. If angle informati...
 2.4.35: Solve each right triangle. In each case, C = 90. If angle informati...
 2.4.36: Solve each right triangle. In each case, C = 90. If angle informati...
 2.4.37: Solve each right triangle. In each case, C = 90. If angle informati...
 2.4.38: Solve each right triangle. In each case, C = 90. If angle informati...
 2.4.39: Solve each right triangle. In each case, C = 90. If angle informati...
 2.4.40: Solve each right triangle. In each case, C = 90. If angle informati...
 2.4.41: Concept Check Answer each question. What is the meaning of the term...
 2.4.42: Concept Check Answer each question. Can an angle of elevation be mo...
 2.4.43: Concept Check Answer each question. Why does the angle of depressio...
 2.4.44: Concept Check Answer each question. Why is angle CAB not an angle o...
 2.4.45: Solve each problem. See Examples 1 4. Height of a Ladder on a Wall ...
 2.4.46: Solve each problem. See Examples 1 4. Distance across a Lake To fin...
 2.4.47: Solve each problem. See Examples 1 4. Height of a Building From a w...
 2.4.48: Solve each problem. See Examples 1 4. Diameter of the Sun To determ...
 2.4.49: Side Lengths of a Triangle The length of the base of an isosceles t...
 2.4.50: Altitude of a Triangle Find the altitude of an isosceles triangle h...
 2.4.51: Solve each problem. See Examples 3 and 4. Height of a Tower The sha...
 2.4.52: Solve each problem. See Examples 3 and 4. Distance from the Ground ...
 2.4.53: Solve each problem. See Examples 3 and 4. Length of a Shadow Suppos...
 2.4.54: Solve each problem. See Examples 3 and 4. Airplane Distance An airp...
 2.4.55: Solve each problem. See Examples 3 and 4. Angle of Depression of a ...
 2.4.56: Solve each problem. See Examples 3 and 4. Height of a Building The ...
 2.4.57: Solve each problem. See Examples 3 and 4. Angle of Elevation of the...
 2.4.58: Solve each problem. See Examples 3 and 4. Angle of Elevation of the...
 2.4.59: Solve each problem. See Examples 3 and 4. Angle of Elevation of the...
 2.4.60: Solve each problem. See Examples 3 and 4. Cloud Ceiling The U.S. We...
 2.4.61: Solve each problem. See Examples 3 and 4. Height of Mt. Everest The...
 2.4.62: Solve each problem. See Examples 3 and 4. Error in Measurement A de...
Solutions for Chapter 2.4: Solutions and Applications of Right Triangles
Full solutions for Trigonometry  11th Edition
ISBN: 9780134217437
Solutions for Chapter 2.4: Solutions and Applications of Right Triangles
Get Full SolutionsSince 62 problems in chapter 2.4: Solutions and Applications of Right Triangles have been answered, more than 20236 students have viewed full stepbystep solutions from this chapter. Trigonometry was written by and is associated to the ISBN: 9780134217437. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 2.4: Solutions and Applications of Right Triangles includes 62 full stepbystep solutions. This textbook survival guide was created for the textbook: Trigonometry, edition: 11.

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

Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

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

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

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

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.
Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

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

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).