 131.1: Copy and complete the spreadsheet above.
 131.2: Describe the relationship among the 306090 triangles with the dim...
 131.3: What patterns do you observe in the ratios of the side measures of ...
 131.4: STANDARDIZED TEST PRACTICE If tan 3, find the value of sin . B A _3...
 131.5: x 23 32
 131.6: 15
 131.7: A = 45, b = 6 8
 131.8: B = 56, c = 6
 131.9: b = 7, c = 18
 131.10: a = 14, b = 13
 131.11: BRIDGES Tom wants to build a rope bridge between his tree house and...
 131.12: AVIATION When landing, a jet will average a 3 angle of descent. Wha...
 131.13: 11
 131.14: 28 21
 131.15: 16
 131.16: 30 10
 131.17: 60 3
 131.18: x 54
 131.19: 23.7
 131.20: 36
 131.21: 16
 131.22: A = 16, c = 14
 131.23: B = 27, b = 7
 131.24: A = 34, a = 10
 131.25: B = 15, c = 25
 131.26: B = 30, b = 11
 131.27: A = 45, c = 7 2
 131.28: SURVEYING A surveyor stands 100 feet from a building and sights the...
 131.29: TRAVEL In a sightseeing boat near the base of the Horseshoe Falls a...
 131.30: 9 5
 131.31: 25
 131.32: 7 1
 131.33: B = 18, a = 15 34
 131.34: A = 10, b = 15
 131.35: b = 6, c = 13 3
 131.36: a = 4, c = 9
 131.37: tan B = _7 8 , b = 7 3
 131.38: sin A = _1 3 , a = 5
 131.39: Using the 306090 triangle shown in the lesson, verify each value....
 131.40: Using the 454590 triangle shown in the lesson, verify each value....
 131.41: At what angle, with respect to the horizontal, is the treadmill bed...
 131.42: If the treadmill bed is 40 inches long, what is the vertical rise w...
 131.43: GEOMETRY Find the area of the regular hexagon with point O as its c...
 131.44: GEOLOGY A geologist measured a 40 of elevation to the top of a moun...
 131.45: OPEN ENDED Draw two right triangles ABC and DEF for which sin A = s...
 131.46: REASONING Find a counterexample to the statement It is always possi...
 131.47: CHALLENGE Explain why the sine and cosine of an acute angle are nev...
 131.48: Writing in Math Use the information on page 759 to explain how trig...
 131.49: ACT/SAT If the secant of angle is _25 7 , what is the sine of angle...
 131.50: ACT/SAT If the secant of angle is _25 7 , what is the sine of angle...
 131.51: surveying band members to find the most popular type of music at yo...
 131.52: surveying people coming into a post office to find out what color c...
 131.53: P(exactly 2 heads) 5
 131.54: P(4 heads) 5
 131.55: P(at least 1 head)
 131.56: y4 64 0 5
 131.57: x5 5x3 4x 0 58
 131.58: d d 132 0 P
 131.59: 5 gallons (_ 4 quarts 1 gallon ) 6
 131.60: 6.8 miles (_5280 feet 1 mile )
 131.61: (__ 2 square meters 5 dollars )30 dollars
 131.62: (_4 liters 5 minutes )60 minutes
Solutions for Chapter 131: Right Triangle Trigonometry
Full solutions for Algebra 2, Student Edition (MERRILL ALGEBRA 2)  1st Edition
ISBN: 9780078738302
Solutions for Chapter 131: Right Triangle Trigonometry
Get Full SolutionsChapter 131: Right Triangle Trigonometry includes 62 full stepbystep solutions. Since 62 problems in chapter 131: Right Triangle Trigonometry have been answered, more than 56046 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their 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.

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

Basis for V.
Independent vectors VI, ... , v d whose linear combinations give each vector in V as v = CIVI + ... + CdVd. V has many bases, each basis gives unique c's. A vector space has many bases!

Dimension of vector space
dim(V) = number of vectors in any basis for V.

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

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!).

GramSchmidt orthogonalization A = QR.
Independent columns in A, orthonormal columns in Q. Each column q j of Q is a combination of the first j columns of A (and conversely, so R is upper triangular). Convention: diag(R) > o.

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

Hilbert matrix hilb(n).
Entries HU = 1/(i + j 1) = Jd X i 1 xj1dx. Positive definite but extremely small Amin and large condition number: H is illconditioned.

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

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).

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)·(b  Ax) = o.

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

Rotation matrix
R = [~ CS ] rotates the plane by () and R 1 = RT rotates back by (). Eigenvalues are eiO and eiO , eigenvectors are (1, ±i). c, s = cos (), sin ().

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

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

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

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

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

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