Advertisements
Advertisements
Question
Convert the following angles into radian:
40°48′
Solution
We know that, 180° = πc
∴ 1° = `(pi/180)^"c"`
∴ 40°48′ = 40° + 48'
= `40^circ + (48/60)^circ ...[∵ 1^circ = 60 "'" "so", 1"'" = (1/60)^circ]`
= `40^circ + (4/5)^circ`
= `(40 + 4/5)^circ`
= `((5 xx 40 + 4)/5)^circ`
= `((200 + 4)/5)^circ`
= `(204/5)^circ`
= `(204/5 xx pi/180)^"c"`
= `(cancel(204)^102/5 xx pi/cancel(180)_90)^"c"`
`= (cancel(102)^51/5 xx pi/cancel(90)_45)^c`
`= (51/5 xx pi/45)^c`
`= (51 pi)/225`
`= (17pi)/75`
APPEARS IN
RELATED QUESTIONS
Convert the following angle into radian:
85°
Convert the following angles into radian:
65°30′
Convert the following angles into radian:
75°30′
Convert the following angles in degree.
`(7pi^"c")/12`
Convert the following angles in degree:
`(11pi^"c")/18`
Express the following angle in degree, minute and second:
(183.7)°
Express the following angle in degree, minute and second:
(245.33)°
Express the following angle in degree, minute and second:
`(1/5)^"c"`
In ∆ABC, if m∠A = `(7pi^"c")/36`, m∠B = 120°, find m∠C in degree and radian.
Two angles of a triangle are `(5pi^"c")/9` and `(5pi^"c")/18`. Find the degree and radian measures of third angle.
In a right angled triangle, the acute angles are in the ratio 4:5. Find the angles of the triangle in degrees and radians.
The measures of the angles of a triangle are in the ratio 3:7:8. Find their measures in degrees and radians.
In a cyclic quadrilateral two adjacent angles are 40° and `pi^"c"/3`. Find the angles of the quadrilateral in degrees.
One angle of a quadrilateral has measure `(2pi^"c")/5` and the measures of other three angles are in the ratio 2 : 3 : 4. Find their measures in degree and radian.
Find the degree and radian measure of exterior and interior angle of a regular hexagon
Find the degree and radian measure of exterior and interior angle of a regular Heptagon.
Select the correct option from the given alternatives :
`((22pi)/15)^"c"` is equal to
Select the correct option from the given alternatives :
A horse is tied to a post by a rope. If the horse moves along a circular path, always keeping the rope tight and describes 88 metres when it traces the angle of 72° at the centre, then the length of the rope is
Select the correct option from the given alternatives :
A pendulum of 14 cm long oscillates through an angle of 12°, then the angle of the path described by its extremities is
Select the correct option from the given alternatives :
20 metres of wire is available for fencing off a flower-bed in the form of a circular sector of radius 5 metres, then the maximum area (in sq. m.) of the flower-bed is
Select the correct option from the given alternatives :
If the angles of a triangle are in the ratio 1 : 2 : 3, then the smallest angle in radian is ______.
Select the correct option from the given alternatives :
Find the measure of the angle between hour-hand and the minute hand of a clock at twenty minutes past two.
Answer the following :
Find the number of sides of a regular polygon, if each of its interior angle is `(3pi^"c")/4`.
Answer the following :
A wire of length 10 cm is bent so as to form an arc of a circle of radius 4 cm. What is the angle subtended at the centre in degree ?
Show that the minute-hand of clock gains 5°30' on the hour-hand in one minute.
Answer the following :
A train is running on a circular track of radius 1 km at the rate of 36 km per hour. Find the angle, to the nearest minute, through which it will turn in 30 seconds.
