Advertisements
Advertisements
Question
The measures of the angles of a triangle are in the ratio 3:7:8. Find their measures in degrees and radians.
Solution
The measures of the angles of the triangle are in the ratio 3:7:8.
Let the measures of the angles of the triangle in degrees be 3k, 7k and 8k, where k is a constant.
∴ 3k + 7k + 8k = 180° ...[Sum of the angles of a triangle is 180°]
∴ 18k = 180°
∴ k = 10°
∴ The measures of the angles in degrees are
3k = 3° x 10° = 30°,
7k = 7° x 10° = 70° and
8k = 8° x 10° = 80°.
We know that θ° = `(theta xx pi/180)^"c"`
∴ The measures of the angles in radians are
30° = `(30 xx pi/180)^"c" = (pi/6)^"c"`
70° = `(70 xx pi/180)^"c" = ((7pi)/18)^"c"`
80° = `(80 xx pi/180)^"c" = ((4pi)/9)^"c"`
APPEARS IN
RELATED QUESTIONS
Convert the following angle into radian:
85°
Convert the following angles into radian:
75°30′
Convert the following angles into radian:
40°48′
Convert the following angles in degree.
`(7pi^"c")/12`
Convert the following angles in degree:
5c
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.
The measures of the angles of a triangle are in A.P. and the greatest is 5 times the smallest (least). Find the angles in degrees and radian.
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 pentagon.
Find the degree and radian measure of exterior and interior angle of a regular Heptagon.
Find the degree and radian measure of exterior and interior angle of a regular Octagon.
A pendulum of length 14 cm oscillates through an angle of 18°. Find the length of its path.
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 :
If the angles of a triangle are in the ratio 1 : 2 : 3, then the smallest angle in radian is ______.
Answer the following :
Find the radius of the circle in which central angle of 60° intercepts an arc of length 37.4 cm.
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.
