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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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BuyFindarrow_forward

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

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.

To determine

To find:

The measure of each indicated angle of the following triangle,

Explanation

Consider the following figure,

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

cosθ=adjacenthypotenuseθ=cos1(adjacenthypotenuse) and sinθ=oppositehypotenuseθ=sin1(oppositehypotenuse)

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

Then 2 is the length of the leg adjacent to α and 2 is the length of leg opposite to β.

The Pythagorean theorem is given below,

(hypotenuse)2=(lengthofoneleg)2+(lengthofotherleg)2

Substitute the values of hypotenuse=c,lengthofoneleg=3andlengthofotherleg=2 to get the following,

(c)2=(3)2+(2)2c2=3+2c2=5c=5

Hence 5 is the length of leg hypotenuse

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Chapter 11 Solutions

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