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

Question

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Answer 1

Question

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 11.CT, Problem 1CT

To determine

a

To express:

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

Expert Solution

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.

To determine

b.

To express:

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

Expert Solution

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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3. Construct a triangle in the Poincare plane with all sides equal to ln(2). (Hint: Use the fact that, the circle with center (0,a) and radius ln(r), r>1 in the Poincaré plane is equal to the point set { (x,y) : x^2+(y-1/2(r+1/r)a)^2=1/4(r-1/r)^2a^2 }

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Answer 2

Question

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 11.CT, Problem 1CT

To determine

a

To express:

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

Expert Solution

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.

To determine

b.

To express:

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

Expert Solution

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.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 11.CT, Problem 1CT

To determine

a

To express:

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

Expert Solution

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.

To determine

b.

To express:

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

Expert Solution

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.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 11.CT, Problem 1CT

To determine

a

To express:

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

Expert Solution

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.

To determine

b.

To express:

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

Expert Solution

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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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 11.CT, Problem 1CT

To determine

a

To express:

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

Expert Solution

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.

To determine

b.

To express:

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

Expert Solution

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.

Answer 6

Chapter 11.CT, Problem 1CT

To determine

a

To express:

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

Expert Solution

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.

Answer 7

Chapter 11.CT, Problem 1CT

To determine

a

To express:

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

Answer 8

Expert Solution

Answer to Problem 1CT

Solution:

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

Answer 9

Expert Solution

Answer 10

Expert Solution

Answer 11

Expert Solution

Answer 12

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.

Answer 13

To determine

b.

To express:

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

Expert Solution

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.

Answer 14

To determine

b.

To express:

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

Answer 15

Expert Solution

Answer to Problem 1CT

Solution:

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

Answer 16

Expert Solution

Answer 17

Expert Solution

Answer 18

Expert Solution

Answer 19

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.

Answer 20

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 - Prob. 9E Ch. 11.1 - Prob. 10E

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

Videos

a

To express:

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

Answer to Problem 1CT

Explanation of Solution

b.

To express:

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

Answer to Problem 1CT

Explanation of Solution

Want to see more full solutions like this?

Chapter 11 Solutions

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

Videos

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

Answer to Problem 1CT

Explanation of Solution

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

Answer to Problem 1CT

Explanation of Solution

Want to see more full solutions like this?

Chapter 11 Solutions

a

To express:

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

b.

To express:

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