Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015

1st Edition

ISBN: 9781680331165

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Houghton Mifflin Harcourt

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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 3, Problem 12CT

To determine

To calculate: The width and the height of the TV.

Expert Solution & Answer

Answer to Problem 12CT

The required width and height of the TV are 27.84 inches and 15.66 inches respectively.

Explanation of Solution

Given information:

The ratio of the screen’s width to its height = 16:9

Width of the screen = 32 inches

Formula used:

Pythagoras theorem:

For a right-angle triangle the Pythagoras formula is,

(hypotenuse)2=(perpendicular)2+(base)2

Calculation:

The given ratio of the screen’s width to its height is 16:9 .

Consider the width and height of the TV be 16x and 9x respectively.

To find the width and height of the TV, use Pythagoras theorem (hypotenuse)2=(perpendicular)2+(base)2 .

Substitute 32 for hypotenuse, 16x for perpendicular and 9x for base in the above formula and simplify.

322=(16x)2+(9x)2256x2+81x2=1024337x2=1024

Simplify further.

337x2337=1024337x2=3.03x=±1.74

Since, x is a factor of the dimensions of the TV;

So, it cannot be negative

Thus, x=1.74

Now, the width of the TV is

16x=(16×1.74) inches=27.84 inches

And, the height of the TV is

9x=(9×1.74) inches=15.66 inches

Hence, the required width and height of the TV are 27.84 inches and 15.66 inches respectively.

Chapter 3, Problem 11CT

Chapter 3, Problem 13CT

Chapter 3 Solutions

Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015

Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E

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