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1.

The measure of one angle of a trangle is `65^(@)` and other angle is `(pi)/(12)`, then determine the sexagesimal value and circular value of third angle.

Answer» `(pi)/(12) = (180^(@))/(12) =15^(@)`
` therefore "the third angle" = 180^(@) - (65^(@) + 15^(@)) = 180^(@) -80^(@) = 100^(@)`
` = 100^(@)xx(pi)/(180^(@)) = (5pi)/(9)`
Hence the third angle is `100^(@) or (5pi)/(9)`.
Discussion
2.

If the ratio of three angles of a triangle is 2 : 3 : 4, then determine the circular value of the greatest angle .

Answer» Let the angles be `2x^(@) , 3x^(@) and 4x^(@)`.
`therefore 2x^(@) + 3x^(@) + 4x^(@) = 180 `
or , `9x^(@) = 180^(@) or, x^(@) = (180^(@))/(9) = 20^(@)`.
`therefore" the greatest angle" = 4x^(@) = 4 xx 20^(@) = 80^(@)`
` =80^(@) xx (pi)/(180^(@)) = (4pi)/(9)`
Discussion
3.

In a circle, if an are of length 220 cm subtends an angle of measure `63^(@)` at the centre ,then determine the radius of the circle.

Answer» `63^(@)` is made by the are 220 cm
`therefore 1^(@)" is made is by are" (220)/(63)` cm
`therefore 360^(@)"is made by the are" (220xx360)/(63) cm =(8800)/(7) cm`
`therefore "the perimeter of the circle" =(8800)/(7)cm`
Let r be the radius of the circule.
`therefore 2pi=(8800)/(7) or, 2xx(22)/(7)xxr=(8800)/(7)` or, r=200.
Hence the radius of the circle =200 cm.
Discussion