Scales Of Cords

SCALES OF CORDS

[caption id="attachment_4427" align="aligncenter" width="567"] scale of cords[/caption]

 

CONSTRUCTION:

1. Drew sector of a circle of 90^. with 'OA' radius. ('OA' any convenient distance )


2. Divide this angle into nine parts of 10^. each.


3. Name as shown from the end 'a' upwards.


4. From 'A' ass center, with cords of each angle as radius drew arcs downwards up to 'AO' line or it's extension and from a scale with proper labeling as shown.

As card length is used to measure & construct different angle it is called the scale of cords.

1. Construct any triangle and measure its angles by using a scale of cords.

CONSTRUCTION:

First prepare the scale of cords for the problem. Then construct a triangle of given sides. (You are supposed to measure angles x,y and z)

To measure angle at x:

Take O-A distance in compass from cords scale and mark it on the lower side of the triangle as shown from corner x. Name O & A as shown. Then O as center, O-A radius drew an arc up to the upper adjacent side. Name the point B. Take A-B cord in compass and place on scale cords from zero. It will give the value of angle at x.

To  measure angle at y:

Repeat the same process from O₁ drew an arc with radius O₁A₁. Place cord A₁B₁ on scale and get angle at y.

To measure angle at z:

Subtract the sum of these two angles from to get an angle at z.



 

angle at Z = 180 - ( 55 + 30 ) = 95º

2. Construct 25^. and 115^. angles with a horizontal line, by using the scale of cords.

CONSTRUCTION:

First prepare the scale of cords for the problem. Then drew a horizontal line. Mark point O on it.

To construct 25^. angle at O.

Take O-A distance in compass from cords scale and mark it on the line drawn, from O Name O& A as shown Then O as center, O-A radius drew an arc upward. Take a cord length of 25^. angle from a scale of cords in compass and from A cut the arc at point B join B with O.The angle AOB is thus 25^.

To construct 115^. angle at O.

This scale can measure or construct angles up to 90^. only directly. Hence subtract 115^. from 180^. we get 75^. angle, which can be constructed with this scale. Extend the previous arc of OA radius and taking cord length of 75^. in compass cut this arc at B₁ with A as center. Join B₁ with O.Now angle AOB₁ is 75^. and COB₁ is 115.

 

 

To construct 115º at O

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