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Math
GeometryElementary Geometry for College Students6th Edition

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Chapter 11.2, Problem 28E
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Elementary Geometry for College St...

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

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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In Exercise 23 to 28, use either the sine ratio or the cosine ratio as needed to find the measure of each indicated angle to the nearest degree.

Chapter 11.2, Problem 28E, In Exercise 23 to 28, use either the sine ratio or the cosine ratio as needed to find the measure of

To determine

To find:

The measure of each indicated angle of the following triangle,

Elementary Geometry for College Students, Chapter 11.2, Problem 28E

Explanation

Consider the following figure,

General formula for cosine ratio and sin ratio is given below,

cosθ=adjacenthypotenuseθ=cos−1(adjacenthypotenuse) and sinθ=oppositehypotenuseθ=sin−1(oppositehypotenuse)

In a rectangle opposite sides are equal. That is, AD=BC=8 in. and CD=AB=6 in.

The Pythagorean theorem is given below,

(BD)2=(CD)2+(BC)2

Substitute the values of AD=BC=8 in. and CD=AB=6 in. to get the following,

(BD)2=(6)2+(8)2(BD)2=36+64(BD)2=100BD=10 in.

Hence 10 in. is the length of leg hypotenuse.

From the given figure the value 10 in. is the hypotenuse value since it is opposite to right angle.

Then 6 in. is the length of the leg adjacent to α and 6 in. is the length of leg opposite to β. Then 8 in. is the length of the leg adjacent to θ and 8 in. is the length of leg opposite to ϕ.

Therefore,

cosα=610cosα=35α=cos−1(35)

Using a graphing calculator in degree mode, follow the following key sequence,

cos−1→(→3→/→5→)→enter→53∘

So the value of α is given below,

α=53∘

Therefore,

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Sect-11.1 P-1ESect-11.1 P-2ESect-11.1 P-3ESect-11.1 P-4ESect-11.1 P-5ESect-11.1 P-6ESect-11.1 P-7ESect-11.1 P-8ESect-11.1 P-9ESect-11.1 P-10E
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