hi i need this question solved, lately i been getting the wrong answer from here please. Find length x.All dimensions are in inches. 12. Find length x.All dimensions are in inches.1.620 DIA2.400-4°50-DIA

Definition of Trigonometric identities sin(x)=Opposite sideHypotenuse and cos(x)=Adjacent…

Answered: 12. Find length x. All dimensions are…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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hi i need this question solved, lately i been getting the wrong answer from here please.

Find length x.
All dimensions are in inches.

12. Find length x.
All dimensions are in inches.
1.620 DIA
2.400
-4°50-
DIA

Expert Solution

Step 1

Definition of Trigonometric identities

$\sin (x) = \frac{O p p o s i t e s i d e}{H y p o t e n u s e}$ and $\cos (x) = \frac{A d j a c e n t s i d e}{H y p o t e n u s e}$ and $\tan (x) = \frac{O p p o s i t e s i d e}{A d j a c e n t s i d e}$

Where $x$ is the angle whose trigonometric value is to be evaluated and the adjacent and opposite sides are the sides adjacent and opposite to the angle $x$ considered inside a right-angled triangle.

Step 2

Consider the figure shown below

Consider the small right-angled triangle constructed by drawing the red horizontal line. The angle $a$ will be half the angle of $40^{°} 50^{'}$ . The given angle in radians will be

$40^{°} 50^{'} = {(40 + \frac{50}{60})}^{°} = {(\frac{245}{6})}^{°} = {(\frac{245}{6} x \frac{π}{180})}^{c} \approx 0 . 7127^{c}$

So the angle $a$ in radians will be

$a = \frac{0.7127}{2} = 0 . 3563^{c}$

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