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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
Publisher: Cengage Learning
ISBN: 9781285195698
BuyFind

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
Publisher: Cengage Learning
ISBN: 9781285195698

Solutions

Chapter
Section
Chapter 11.CT, Problem 1CT
Textbook Problem

For the right triangle shown, express each of the following in terms of a, b, and c:

a) sin α_______
b) tan Β_______

Chapter 11.CT, Problem 1CT, For the right triangle shown, express each of the following in terms of a, b, and c: a sin _______ b

Expert Solution
To determine

a

To express:

The ratio sin α in terms of a, b, and c.

Answer to Problem 1CT

Solution:

The value of sin α in terms of a, b, and c is sin α = ac.

Explanation of Solution

Definition:

In a right triangle, the sine ratio for an acute angle is the ratio oppsite sidehypotenuse.

Given:

The right triangle shown below

Elementary Geometry for College Students, Chapter 11.CT, Problem 1CT , additional homework tip  1

From the figure given,

For the angle α, opposite side = a and hypotenuse = c.

By the definition, sin α = oppsite sidehypotenuse

sin α = ac

Conclusion:

The value of sin α in terms of a, b, and c is sin α = ac.

Expert Solution
To determine

b.

To express:

The given tan β in terms of a, b, and c.

Answer to Problem 1CT

Solution:

The value of tan β in terms of a, b, and c is tan β = ba.

Explanation of Solution

Definition:

In a right triangle, the tangent ratio for an acute angle is the ratio oppsite sideadjacent side.

Given:

The right triangle shown below

Elementary Geometry for College Students, Chapter 11.CT, Problem 1CT , additional homework tip  2

Calculation:

For the angle β, opposite side = b and adjacent side = a.

By the definition, tan β= oppsite sideadjacent side

tan β = ba

Conclusion:

The value of tan β in terms of a, b, and c is tan β =ba.

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Chapter 11 Solutions

Elementary Geometry for College Students
Show all chapter solutions
Ch. 11.1 - In Exercises 7 to 14, use either Table 11.2 or a...Ch. 11.1 - In Exercises 7 to 14, use either Table 11.2 or a...Ch. 11.1 - In Exercises 7 to 14, use either Table 11.2 or a...Ch. 11.1 - In Exercises 7 to 14, use either Table 11.2 or a...Ch. 11.1 - In Exercises 15 to 20, find the lengths of the...Ch. 11.1 - In Exercises 15 to 20, find the lengths of the...Ch. 11.1 - In Exercises 15 to 20, find the lengths of the...Ch. 11.1 - In Exercises 15 to 20, find the lengths of the...Ch. 11.1 - In Exercises 15 to 20, find the lengths of the...Ch. 11.1 - In Exercises 15 to 20, find the lengths of the...Ch. 11.1 - In Exercises 21 to 26, find the measures of the...Ch. 11.1 - In Exercises 21 to 26, find the measures of the...Ch. 11.1 - In Exercises 21 to 26, find the measures of the...Ch. 11.1 - In Exercises 21 to 26, find the measures of the...Ch. 11.1 - In Exercises 21 to 26, find the measures of the...Ch. 11.1 - In Exercises 21 to 26, find the measures of the...Ch. 11.1 - In Exercises 27 to 34, use the drawings, where...Ch. 11.1 - In Exercises 27 to 34, use the drawings, where...Ch. 11.1 - In Exercises 27 to 34, use the drawings, where...Ch. 11.1 - In Exercises 27 to 34, use the drawings, where...Ch. 11.1 - In Exercises 27 to 34, use the drawings, where...Ch. 11.1 - In Exercises 27 to 34, use the drawings, where...Ch. 11.1 - In Exercises 27 to 34, use the drawings, where...Ch. 11.1 - In Exercises 27 to 34, use the drawings, where...Ch. 11.1 - For Exercises 35 to 38, make drawings as needed....Ch. 11.1 - For Exercises 35 to 38, make drawings as needed....Ch. 11.1 - For Exercises 35 to 38, make drawings as needed....Ch. 11.1 - For Exercises 35 to 38, make drawings as needed....Ch. 11.1 - For Exercises 35 to 38, make drawings as needed....Ch. 11.2 - In Exercises 1 to 6, find cos and cos.Ch. 11.2 - In Exercises 1 to 6, find cos and cos.Ch. 11.2 - In Exercises 1 to 6, find cos and cos.Ch. 11.2 - In Exercises 1 to 6, find cos and cos.Ch. 11.2 - In Exercises 1 to 6, find cos and cos.Ch. 11.2 - In Exercises 1 to 6, find cos and cos.Ch. 11.2 - For the triangles in Exercises 1 to 6, a why does...Ch. 11.2 - Using the right triangle from Exercise 1, show...Ch. 11.2 - In Exercise 9 to 16, use a calculator to find the...Ch. 11.2 - In Exercise 9 to 16, use a calculator to find the...Ch. 11.2 - In Exercise 9 to 16, use a calculator to find the...Ch. 11.2 - In Exercise 9 to 16, use a calculator to find the...Ch. 11.2 - In Exercise 9 to 16, use a calculator to find the...Ch. 11.2 - In Exercise 9 to 16, use a calculator to find the...Ch. 11.2 - In Exercise 9 to 16, use a calculator to find the...Ch. 11.2 - In Exercise 9 to 16, use a calculator to find the...Ch. 11.2 - In Exercise 17 to 22, use either the sine ratio or...Ch. 11.2 - In Exercise 17 to 22, use either the sine ratio or...Ch. 11.2 - In Exercise 17 to 22, use either the sine ratio or...Ch. 11.2 - In Exercise 17 to 22, use either the sine ratio or...Ch. 11.2 - In Exercise 17 to 22, use either the sine ratio or...Ch. 11.2 - In Exercise 17 to 22, use either the sine ratio or...Ch. 11.2 - In Exercise 23 to 28, use either the sine ratio or...Ch. 11.2 - In Exercise 23 to 28, use either the sine ratio or...Ch. 11.2 - In Exercise 23 to 28, use either the sine ratio or...Ch. 11.2 - In Exercise 23 to 28, use either the sine ratio or...Ch. 11.2 - In Exercise 23 to 28, use either the sine ratio or...Ch. 11.2 - In Exercise 23 to 28, use either the sine ratio or...Ch. 11.2 - In Exercise 29 to 37, angle measures should be...Ch. 11.2 - In Exercise 29 to 37, angle measures should be...Ch. 11.2 - In Exercise 29 to 37, angle measures should be...Ch. 11.2 - In Exercise 29 to 37, angle measures should be...Ch. 11.2 - In Exercise 29 to 37, angle measures should be...Ch. 11.2 - In Exercise 29 to 37, angle measures should be...Ch. 11.2 - In Exercise 29 to 37, angle measures should be...Ch. 11.2 - In Exercise 29 to 37, angle measures should be...Ch. 11.2 - In Exercise 29 to 37, angle measures should be...Ch. 11.2 - In the right circular cone, a Find r correct to...Ch. 11.2 - In parallelogram ABCD, find to the nearest degree:...Ch. 11.2 - A ladder of length AB is carried horizontally...Ch. 11.2 - Use the drawing provided to show that the area of...Ch. 11.2 - For Exercise 42 and 43, use the drawing and the...Ch. 11.2 - For Exercise 42 and 43, use the drawing and the...Ch. 11.2 - In regular pentagon ABCDE, each radius has length...Ch. 11.2 - Consider regular pentagon ABCDE of Exercise 44. In...Ch. 11.3 - In Exercises 1 to 4, find tan and tan for each...Ch. 11.3 - In Exercises 1 to 4, find tan and tan for each...Ch. 11.3 - In Exercises 1 to 4, find tan and tan for each...Ch. 11.3 - In Exercises 1 to 4, find tan and tan for each...Ch. 11.3 - In Exercises 5 to 10, find the value or expression...Ch. 11.3 - In Exercises 5 to 10, find the value or expression...Ch. 11.3 - In Exercises 5 to 10, find the value or expression...Ch. 11.3 - In Exercises 5 to 10, find the value or expression...Ch. 11.3 - In Exercises 5 to 10, find the value or expression...Ch. 11.3 - In Exercises 5 to 10, find the value or expression...Ch. 11.3 - In Exercises 11 to 14, use a calculator to find...Ch. 11.3 - In Exercises 11 to 14, use a calculator to find...Ch. 11.3 - In Exercises 11 to 14, use a calculator to find...Ch. 11.3 - In Exercises 11 to 14, use a calculator to find...Ch. 11.3 - In Exercises 15 to 20, use the sine, cosine, or...Ch. 11.3 - In Exercises 15 to 20, use the sine, cosine, or...Ch. 11.3 - In Exercises 15 to 20, use the sine, cosine, or...Ch. 11.3 - In Exercises 15 to 20, use the sine, cosine, or...Ch. 11.3 - In Exercises 15 to 20, use the sine, cosine, or...Ch. 11.3 - In Exercises 15 to 20, use the sine, cosine, or...Ch. 11.3 - In Exercises 21 to 26, use the sine, cosine, or...Ch. 11.3 - In Exercises 21 to 26, use the sine, cosine, or...Ch. 11.3 - In Exercises 21 to 26, use the sine, cosine, or...Ch. 11.3 - In Exercises 21 to 26, use the sine, cosine, or...Ch. 11.3 - In Exercises 21 to 26, use the sine, cosine, or...Ch. 11.3 - In Exercises 21 to 26, use the sine, cosine, or...Ch. 11.3 - In Exercises 27 to 32, use a calculator and...Ch. 11.3 - In Exercises 27 to 32, use a calculator and...Ch. 11.3 - In Exercises 27 to 32, use a calculator and...Ch. 11.3 - In Exercises 27 to 32, use a calculator and...Ch. 11.3 - In Exercises 27 to 32, use a calculator and...Ch. 11.3 - In Exercises 27 to 32, use a calculator and...Ch. 11.3 - In Exercises 33 to36, we expand the list of...Ch. 11.3 - In Exercises 33 to 36, we expand the list of...Ch. 11.3 - In Exercises 33 to 36, we expand the list of...Ch. 11.3 - In Exercises 33 to 36, we expand the list of...Ch. 11.3 - In Exercises 37 to 43, angle measures should be...Ch. 11.3 - In Exercises 37 to 43, angle measures should be...Ch. 11.3 - In Exercises 37 to 43, angle measures should be...Ch. 11.3 - In Exercises 37 to 43, angle measures should be...Ch. 11.3 - In Exercises 37 to 43, angle measures should be...Ch. 11.3 - In Exercises 37 to 43, angle measures should be...Ch. 11.3 - In Exercises 37 to 43, angle measures should be...Ch. 11.3 - In the triangle shown, find each measure to the...Ch. 11.3 - At an altitude of 12,000 ft, a pilot sees two...Ch. 11.3 - Consider the regular square pyramid shown. a Find...Ch. 11.3 - Consider the regular square pyramid shown. a Find...Ch. 11.4 - In Exercises 1 and 2, use the given information to...Ch. 11.4 - In Exercises 1 and 2, use the given information to...Ch. 11.4 - In Exercises 3 and 4, state the form of the Law of...Ch. 11.4 - In Exercises 3 and 4, state the form of the Law of...Ch. 11.4 - In Exercises 5 and 6, state the form of the Law of...Ch. 11.4 - In Exercises 5 and 6, state the form of the Law of...Ch. 11.4 - In Exercises 7 and 8, state the form of the Law of...Ch. 11.4 - In Exercises 7 and 8, state the form of the Law of...Ch. 11.4 - For ABC not shown, suppose you know that...Ch. 11.4 - For ABC not shown, suppose you know that...Ch. 11.4 - In Exercises 11 to 14, find the area of each...Ch. 11.4 - In Exercises 11 to 14, find the area of each...Ch. 11.4 - In Exercises 11 to 14, find the area of each...Ch. 11.4 - In Exercises 11 to 14, find the area of each...Ch. 11.4 - In Exercises 15 and 16, find the area of the given...Ch. 11.4 - In Exercises 15 and 16, find the area of the given...Ch. 11.4 - In Exercises 17 to 22, use a form of the Law of...Ch. 11.4 - In Exercises 17 to 22, use a form of the Law of...Ch. 11.4 - In Exercises 17 to 22, use a form of the Law of...Ch. 11.4 - In Exercises 17 to 22, use a form of the Law of...Ch. 11.4 - In Exercises 17 to 22, use a form of the Law of...Ch. 11.4 - In Exercises 17 to 22, use a form of the Law of...Ch. 11.4 - In Exercises 23 to 28, use a form of the Law of...Ch. 11.4 - In Exercises 23 to 28, use a form of the Law of...Ch. 11.4 - In Exercises 23 to 28, use a form of the Law of...Ch. 11.4 - In Exercises 23 to 28, use a form of the Law of...Ch. 11.4 - In Exercises 23 to 28, use a form of the Law of...Ch. 11.4 - In Exercises 23 to 28, use a form of the Law of...Ch. 11.4 - In Exercises 29 to 34, use the Law of Sines or the...Ch. 11.4 - In Exercises 29 to 34, use the Law of Sines or the...Ch. 11.4 - In Exercises 29 to 34, use the Law of Sines or the...Ch. 11.4 - In Exercises 29 to 34, use the Law of Sines or the...Ch. 11.4 - In Exercises 29 to 34, use the Law of Sines or the...Ch. 11.4 - In Exercises 29 to 34, use the Law of Sines or the...Ch. 11.4 - For the triangle shown, the area is exactly...Ch. 11.4 - For the triangle shown, use the Law of Cosines to...Ch. 11.4 - In the support structure for the Ferris wheel,...Ch. 11.4 - Show that the form of the Law of Cosines written...Ch. 11.4 - Explain why the area of the parallelogram shown is...Ch. 11.4 - Find the area of MNPQifa=8cm,b=12cm,and=70. Answer...Ch. 11.4 - Find the area of MNPQifa=6.3cm,b=8.9cm,and=67.5....Ch. 11.4 - The sides of a rhombus have length a. Two adjacent...Ch. 11.4 - Two sides of a triangle have measures a inches and...Ch. 11.4 - Use Theorem 11.4.1 to show that the area of an...Ch. 11.CR - In Exercises 1 to 4, state the ratio needed, and...Ch. 11.CR - In Exercises 1 to 4, state the ratio needed, and...Ch. 11.CR - In Exercises 1 to 4, state the ratio needed, and...Ch. 11.CR - In Exercises 1 to 4, state the ratio needed, and...Ch. 11.CR - In Exercises 5 to 8, state the ratio needed, and...Ch. 11.CR - In Exercises 5 to 8, state the ratio needed, and...Ch. 11.CR - In Exercises 5 to 8, state the ratio needed, and...Ch. 11.CR - In Exercises 5 to 8, state the ratio needed, and...Ch. 11.CR - In Exercises 9 to 12, use the Law of Sines or the...Ch. 11.CR - In Exercises 9 to 12, use the Law of Sines or the...Ch. 11.CR - In Exercises 9 to 12, use the Law of Sines or the...Ch. 11.CR - In Exercises 9 to 12, use the Law of Sines or the...Ch. 11.CR - In Exercises 13 to 17, use the Law of Sines or the...Ch. 11.CR - In Exercises 13 to 17, use the Law of Sines or the...Ch. 11.CR - In Exercises 13 to 17, use the Law of Sines or the...Ch. 11.CR - In Exercises 13 to 17, use the Law of Sines or the...Ch. 11.CR - In Exercises 13 to 17, use the Law of Sines or the...Ch. 11.CR - In Exercise 18 to 20, prove each statement without...Ch. 11.CR - In Exercise 18 to 20, prove each statement without...Ch. 11.CR - In Exercise 18 to 20, prove each statement without...Ch. 11.CR - In exercises 21 to 30. Use the drawings. Where...Ch. 11.CR - In exercises 21 to 30. Use the drawings. Where...Ch. 11.CR - In exercises 21 to 30. Use the drawings. Where...Ch. 11.CR - In Exercises 21 to 30, use the drawings, where...Ch. 11.CR - In Exercises 21 to 30, use the drawings, where...Ch. 11.CR - In Exercises 21 to 30, use the drawings, where...Ch. 11.CR - In Exercises 21 to 30, use the drawings, where...Ch. 11.CR - In Exercises 21 to 30, use the drawings, where...Ch. 11.CR - In Exercises 21 to 30, use the drawings, where...Ch. 11.CR - In Exercises 21 to 30, use the drawings, where...Ch. 11.CR - If sin=725, find cos and sec.Ch. 11.CR - If tan=1160, find sec and cot.Ch. 11.CR - If cot=2120, find csc and sinCh. 11.CR - In a right circular cone, the radius of the base...Ch. 11.CT - For the right triangle shown, express each of the...Ch. 11.CT - For the right triangle shown, express each ratio...Ch. 11.CT - Without using a calculator, find the exact value...Ch. 11.CT - Use your calculator to find each number correct to...Ch. 11.CT - Using your calculator, find to the nearest degree...Ch. 11.CT - Without the calculator, determine which number is...Ch. 11.CT - In the drawing provided, find the value of a to...Ch. 11.CT - In the drawing provided, find the value of y to...Ch. 11.CT - In the drawing provided, find the measure of to...Ch. 11.CT - Using the drawing below, classify each statement...Ch. 11.CT - A kite is flying at an angle of elevation of 670...Ch. 11.CT - A roofline shows a span of 12 ft across a sloped...Ch. 11.CT - If sin =12, find: a csc ____________ b...Ch. 11.CT - In a right triangle with acute of measures and ,...Ch. 11.CT - Use one of the three forms for area such as the...Ch. 11.CT - On the basis of the drawing provided, complete the...Ch. 11.CT - On the basis of the drawing provided, complete...Ch. 11.CT - Use the Law of Sines or the Law of Cosines to find...Ch. 11.CT - Use the Law of Sines or the Law of Cosines to find...Ch. 11.CT - Each apothem of regular pentagon ABCDE has length...

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