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6th Edition

Daniel C. Alexander + 1 other

Publisher: Cengage Learning

ISBN: 9781285195698

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_______ |

Expert Solution

To determine

a

**To express:**

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

**Solution:**

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

**Definition:**

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

**Given:**

The right triangle shown below

From the figure given,

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

By the definition, sin α =

sin α =

**Conclusion:**

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

Expert Solution

To determine

b.

**To express:**

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

**Solution:**

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

**Definition:**

In a right triangle, the tangent ratio for an acute angle is the ratio

**Given:**

The right triangle shown below

**Calculation:**

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

By the definition, tan β=

tan β =

**Conclusion:**

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

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Get SolutionsElementary Geometry for College Students

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Ch. 11.1 - In Exercises 1 to 6, find sin and sin for the...Ch. 11.1 - In Exercises 1 to 6, find sin and sin for the...Ch. 11.1 - In Exercises 1 to 6, find sin and sin for the...Ch. 11.1 - In Exercises 1 to 6, find sin and sin for the...Ch. 11.1 - In Exercises 1 to 6, find sin and sin for the...Ch. 11.1 - In Exercises 1 to 6, find sin and sin for the...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 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 - 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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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