 1.2.1: Fill in the blank(s) to correctly complete each sentence. The sum o...
 1.2.2: Fill in the blank(s) to correctly complete each sentence. An isosce...
 1.2.3: Fill in the blank(s) to correctly complete each sentence. An equila...
 1.2.4: Fill in the blank(s) to correctly complete each sentence. If two tr...
 1.2.5: In each figure, find the measures of the numbered angles, given tha...
 1.2.6: In each figure, find the measures of the numbered angles, given tha...
 1.2.7: Name the corresponding angles and the corresponding sides of each p...
 1.2.8: Name the corresponding angles and the corresponding sides of each p...
 1.2.9: Name the corresponding angles and the corresponding sides of each p...
 1.2.10: Name the corresponding angles and the corresponding sides of each p...
 1.2.11: Find the measure of each marked angle. In Exercises 1922, m and n a...
 1.2.12: Find the measure of each marked angle. In Exercises 1922, m and n a...
 1.2.13: Find the measure of each marked angle. In Exercises 1922, m and n a...
 1.2.14: Find the measure of each marked angle. In Exercises 1922, m and n a...
 1.2.15: Find the measure of each marked angle. In Exercises 1922, m and n a...
 1.2.16: Find the measure of each marked angle. In Exercises 1922, m and n a...
 1.2.17: Find the measure of each marked angle. In Exercises 1922, m and n a...
 1.2.18: Find the measure of each marked angle. In Exercises 1922, m and n a...
 1.2.19: Find the measure of each marked angle. In Exercises 1922, m and n a...
 1.2.20: Find the measure of each marked angle. In Exercises 1922, m and n a...
 1.2.21: Find the measure of each marked angle. In Exercises 1922, m and n a...
 1.2.22: Find the measure of each marked angle. In Exercises 1922, m and n a...
 1.2.23: The measures of two angles of a triangle are given. Find the measur...
 1.2.24: The measures of two angles of a triangle are given. Find the measur...
 1.2.25: The measures of two angles of a triangle are given. Find the measur...
 1.2.26: The measures of two angles of a triangle are given. Find the measur...
 1.2.27: The measures of two angles of a triangle are given. Find the measur...
 1.2.28: The measures of two angles of a triangle are given. Find the measur...
 1.2.29: The measures of two angles of a triangle are given. Find the measur...
 1.2.30: The measures of two angles of a triangle are given. Find the measur...
 1.2.31: Concept Check Can a triangle have angles of measures 85 and 100?
 1.2.32: Concept Check Can a triangle have two obtuse angles?
 1.2.33: Concept Check Classify each triangle as acute, right, or obtuse. Al...
 1.2.34: Concept Check Classify each triangle as acute, right, or obtuse. Al...
 1.2.35: Concept Check Classify each triangle as acute, right, or obtuse. Al...
 1.2.36: Concept Check Classify each triangle as acute, right, or obtuse. Al...
 1.2.37: Concept Check Classify each triangle as acute, right, or obtuse. Al...
 1.2.38: Concept Check Classify each triangle as acute, right, or obtuse. Al...
 1.2.39: Concept Check Classify each triangle as acute, right, or obtuse. Al...
 1.2.40: Concept Check Classify each triangle as acute, right, or obtuse. Al...
 1.2.41: Concept Check Classify each triangle as acute, right, or obtuse. Al...
 1.2.42: Concept Check Classify each triangle as acute, right, or obtuse. Al...
 1.2.43: Concept Check Classify each triangle as acute, right, or obtuse. Al...
 1.2.44: Concept Check Classify each triangle as acute, right, or obtuse. Al...
 1.2.45: Angle Sum of a Triangle Use this figure to discuss why the measures...
 1.2.46: Carpentry Technique The following technique is used by carpenters t...
 1.2.47: Find all unknown angle measures in each pair of similar triangles. ...
 1.2.48: Find all unknown angle measures in each pair of similar triangles. ...
 1.2.49: Find all unknown angle measures in each pair of similar triangles. ...
 1.2.50: Find all unknown angle measures in each pair of similar triangles. ...
 1.2.51: Find all unknown angle measures in each pair of similar triangles. ...
 1.2.52: Find all unknown angle measures in each pair of similar triangles. ...
 1.2.53: Find the unknown side lengths in each pair of similar triangles. Se...
 1.2.54: Find the unknown side lengths in each pair of similar triangles. Se...
 1.2.55: Find the unknown side lengths in each pair of similar triangles. Se...
 1.2.56: Find the unknown side lengths in each pair of similar triangles. Se...
 1.2.57: Find the unknown side lengths in each pair of similar triangles. Se...
 1.2.58: Find the unknown side lengths in each pair of similar triangles. Se...
 1.2.59: Solve each problem. See Example 5. Height of a Tree A tree casts a ...
 1.2.60: Solve each problem. See Example 5. Height of a Lookout Tower A fore...
 1.2.61: Solve each problem. See Example 5. Lengths of Sides of a Triangle O...
 1.2.62: Solve each problem. See Example 5. Height of a Lighthouse The Bilox...
 1.2.63: Height of a Building A house is 15 ft tall. Its shadow is 40 ft lon...
 1.2.64: Height of a Carving of Lincoln Assume that Lincoln was 61 3 ft tall...
 1.2.65: In each figure, there are two similar triangles. Find the unknown m...
 1.2.66: In each figure, there are two similar triangles. Find the unknown m...
 1.2.67: In each figure, there are two similar triangles. Find the unknown m...
 1.2.68: In each figure, there are two similar triangles. Find the unknown m...
 1.2.69: Solar Eclipse on Earth The sun has a diameter of about 865,000 mi w...
 1.2.70: Solar Eclipse on Neptune (Refer to Exercise 69.) The suns distance ...
 1.2.71: Solar Eclipse on Mars (Refer to Exercise 69.) The suns distance fro...
 1.2.72: Solar Eclipse on Jupiter (Refer to Exercise 69.) The suns distance ...
 1.2.73: Sizes and Distances in the Sky Astronomers use degrees, minutes, an...
 1.2.74: Estimates of Heights There is a relatively simple way to make a rea...
Solutions for Chapter 1.2: Angle Relationships and Similar Triangles
Full solutions for Trigonometry  11th Edition
ISBN: 9780134217437
Solutions for Chapter 1.2: Angle Relationships and Similar Triangles
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 1.2: Angle Relationships and Similar Triangles includes 74 full stepbystep solutions. This textbook survival guide was created for the textbook: Trigonometry, edition: 11. Since 74 problems in chapter 1.2: Angle Relationships and Similar Triangles have been answered, more than 22663 students have viewed full stepbystep solutions from this chapter. Trigonometry was written by and is associated to the ISBN: 9780134217437.

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

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).

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

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.

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

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 matrix N.
The columns of N are the n  r special solutions to As = O.

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

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

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).

Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or 1) based on the number of row exchanges to reach I.

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.

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.

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!

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Sum V + W of subs paces.
Space of all (v in V) + (w in W). Direct sum: V n W = to}.