Question

Express in Radian the fourth angle of a quadrilateral which has three angles 46 degree 30 minutes 10 seconds 75 degree 44 minutes 45 seconds and 123 degree 9 minute 35 second respectively taking π = 355/113​

Answer 1

Answer:

2

Step-by-step explanation:

Given  

Express in Radian the fourth angle of a quadrilateral which has three angles 46 degree 30 minutes 10 seconds 75 degree 44 minutes 45 seconds and 123

Now the sum of three given angles will be

46° 30´ 10” + 75°44´45” + 123°9´35”

Since 90 degree = 1’30” and 84’ = 1 degree 24”

We get 245 degree 24’30”

Now the sum of all the angles of a quadrilateral is 360 degree.

So fourth angle will be 360 – (245°24’30”)  

Since 360° = 359 degree 59’60” we get 114°35’30”

Now we need to convert it into radians

114 degree 35’30” = 114° + (35 + 30/60)’

= 114 degree(71/120)’ = 114 degree + 71/120 degree

=  (13751 / 120) degree

Since 180° = π radians

13751/120 x π/180 radians

= 13751/120 x 1/180 x 355/113

= 4881605 / 2440800

= 2 Radians