 2.4.2.1.248: Geometry The two equal sides of an isosceles triangle are each 42 c...
 2.4.2.1.249: Geometry An equilateral triangle (one with all sides the same lengt...
 2.4.2.1.250: Geometry The height of a right circular cone is 25.3 centimeters. I...
 2.4.2.1.251: Geometry The diagonal of a rectangle is 348 millimeters, while the ...
 2.4.2.1.252: Length of an Escalator How long should an escalator be if it is to ...
 2.4.2.1.253: Height of a Hill A road up a hill makes an angle of 5.10 with the h...
 2.4.2.1.254: Length of a Rope A 72.5foot rope from the top of a circus tent pol...
 2.4.2.1.255: Angle of a Ladder A ladder is leaning against the top of a 7.0foot...
 2.4.2.1.256: Angle of Elevation If a 73.0foot flagpole casts a shadow 51.0 feet...
 2.4.2.1.257: Angle of Elevation Ifthe angle of elevation of the sun is 63.4 when...
 2.4.2.1.258: Angle of Depression A person standing 150 centimeters from a mirror...
 2.4.2.1.259: Width of a Sand Pile A person standing on top of a 15foot high san...
 2.4.2.1.260: Figure 14 shows the topographic map we used in Example 4 of this se...
 2.4.2.1.261: Figure 14 shows the topographic map we used in Example 4 of this se...
 2.4.2.1.262: Figure 14 shows the topographic map we used in Example 4 of this se...
 2.4.2.1.263: Figure 14 shows the topographic map we used in Example 4 of this se...
 2.4.2.1.264: Distance and Bearing 17 through 22 involve directions in the form o...
 2.4.2.1.265: Distance and Bearing 17 through 22 involve directions in the form o...
 2.4.2.1.266: Distance and Bearing 17 through 22 involve directions in the form o...
 2.4.2.1.267: Distance and Bearing 17 through 22 involve directions in the form o...
 2.4.2.1.268: Distance and Bearing 17 through 22 involve directions in the form o...
 2.4.2.1.269: Distance and Bearing 17 through 22 involve directions in the form o...
 2.4.2.1.270: Distance In Figure 17, a person standing at point A notices that th...
 2.4.2.1.271: Height of an Obelisk Two people decide to find the height of an obe...
 2.4.2.1.272: Qeight of a Tree An ecologist wishes to find the height of a redwoo...
 2.4.2.1.273: Rescue A helicopter makes a forced landing at sea. The last radio s...
 2.4.2.1.274: Height of a Flagpole Two people decide to estimate the height of a ...
 2.4.2.1.275: Height of a Tree To estimate the height of a tree, one person posit...
 2.4.2.1.276: Radius of the Earth A satellite is circling 112 miles above the ear...
 2.4.2.1.277: Distance Suppose Figure 21 is an exaggerated diagram of a plane fiy...
 2.4.2.1.278: Distance A ship is anchored off a long straight shoreline that runs...
 2.4.2.1.279: Distance Pat and Tim position themselves 2.5 miles apart to watch a...
 2.4.2.1.280: Spiral of Roots Figure 22 shows the Spiral of Roots we mentioned in...
 2.4.2.1.281: Spiral of Roots Figure 22 shows the Spiral of Roots we mentioned in...
 2.4.2.1.282: The following problems review material we covered in Section 1.5.Ex...
 2.4.2.1.283: The following problems review material we covered in Section 1.5.Su...
 2.4.2.1.284: Show that each of the following statements is true by transforming ...
 2.4.2.1.285: Show that each of the following statements is true by transforming ...
 2.4.2.1.286: Show that each of the following statements is true by transforming ...
 2.4.2.1.287: Show that each of the following statements is true by transforming ...
 2.4.2.1.288: Show that each of the following statements is true by transforming ...
 2.4.2.1.289: Show that each of the following statements is true by transforming ...
 2.4.2.1.290: One of the items we discussed in this section was topographic maps....
 2.4.2.1.291: Albert lives in New Orleans. At noon on a summer day, the angle of ...
Solutions for Chapter 2.4: Right Triangle Trigonometry
Full solutions for Trigonometry
ISBN: 9780495108351
Solutions for Chapter 2.4: Right Triangle Trigonometry
Get Full SolutionsChapter 2.4: Right Triangle Trigonometry includes 44 full stepbystep solutions. This textbook survival guide was created for the textbook: Trigonometry, edition: . This expansive textbook survival guide covers the following chapters and their solutions. Since 44 problems in chapter 2.4: Right Triangle Trigonometry have been answered, more than 29580 students have viewed full stepbystep solutions from this chapter. Trigonometry was written by and is associated to the ISBN: 9780495108351.

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).

Augmented matrix [A b].
Ax = b is solvable when b is in the column space of A; then [A b] has the same rank as A. Elimination on [A b] keeps equations correct.

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

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

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

Fibonacci numbers
0,1,1,2,3,5, ... satisfy Fn = Fnl + Fn 2 = (A7 A~)I()q A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

Hessenberg matrix H.
Triangular matrix with one extra nonzero adjacent diagonal.

Linear transformation T.
Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

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

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

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(DÂ» 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.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

Reflection matrix (Householder) Q = I 2uuT.
Unit vector u is reflected to Qu = u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q1 = Q.

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