Advertisements
Advertisements
प्रश्न
If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their radii.
Advertisements
उत्तर
Let r1, r2 and 01, 02 be the radii and angles subtended at the centre of two circles, respectively.
Let its radius = r1
l = r1θ1
= r1 `pi/3`
∴ r1 = `(3l)/pi` …(i)
For the second circle,
Let radius = r2
Arc length = l
The angle made by the arc at the centre, θ2 = 75°
= `75 xx π/180` radians
= `(5π)/12` radians
r2 = `(12l)/(5π)`
On dividing equation (i) by equation (ii)
`r^1/r^2 = (3l)/π + (12l)/(5π)`
= `(3l)/πxx(5π)/(12l)` = 5 : 4.
APPEARS IN
संबंधित प्रश्न
Find the radian measure corresponding to the following degree measure:
25°
Find the radian measure corresponding to the following degree measure:
– 47° 30'
Find the degree measure corresponding to the following radian measure `(use pi = 22/7)`
`11/16`
Find the degree measure corresponding to the following radian measure (use `pi= 22/7`).
`(7pi)/6`
Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm
(Use `pi = 22/7`)
Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length
15 cm
Find the degree measure corresponding to the following radian measure:
\[\frac{9\pi}{5}\]
Find the radian measure corresponding to the following degree measure:
300°
Find the radian measure corresponding to the following degree measure: −300°
Find the radian measure corresponding to the following degree measure: 125° 30'
One angle of a triangle \[\frac{2}{3}\] x grades and another is \[\frac{3}{2}\] x degrees while the third is \[\frac{\pi x}{75}\] radians. Express all the angles in degrees.
Find the magnitude, in radians and degrees, of the interior angle of a regular octagon.
Find the magnitude, in radians and degrees, of the interior angle of a regular heptagon.
Find the magnitude, in radians and degrees, of the interior angle of a regular duodecagon.
Let the angles of the quadrilateral be \[\left( a - 3d \right)^\circ, \left( a - d \right)^\circ, \left( a + d \right)^\circ \text{ and }\left( a + 3d \right)^\circ\]
We know: \[a - 3d + a - d + a + d + a - 2d = 360\]
\[ \Rightarrow 4a = 360\]
\[ \Rightarrow a = 90\]
We have:
Greatest angle = 120°
Now,
\[a + 3d = 120\]
\[ \Rightarrow 90 + 3d = 120\]
\[ \Rightarrow 3d = 30\]
\[ \Rightarrow d = 10\]
Hence,
\[\left( a - 3d \right)^\circ, \left( a - d \right)^\circ, \left( a + d \right)^\circ\text{ and }\left( a + 3d \right)^\circ\] are
Angles of the quadrilateral in radians =
The angles of a triangle are in A.P. such that the greatest is 5 times the least. Find the angles in radians.
The number of sides of two regular polygons are as 5 : 4 and the difference between their angles is 9°. Find the number of sides of the polygons.
A rail road curve is to be laid out on a circle. What radius should be used if the track is to change direction by 25° in a distance of 40 metres?
Find the length which at a distance of 5280 m will subtend an angle of 1' at the eye.
The radius of a circle is 30 cm. Find the length of an arc of this circle, if the length of the chord of the arc is 30 cm.
A railway train is travelling on a circular curve of 1500 metres radius at the rate of 66 km/hr. Through what angle has it turned in 10 seconds?
Find the distance from the eye at which a coin of 2 cm diameter should be held so as to conceal the full moon whose angular diameter is 31'.
Find the diameter of the sun in km supposing that it subtends an angle of 32' at the eye of an observer. Given that the distance of the sun is 91 × 106 km.
If the arcs of the same length in two circles subtend angles 65° and 110° at the centre, find the ratio of their radii.
If the angles of a triangle are in A.P., then the measures of one of the angles in radians is
The angle between the minute and hour hands of a clock at 8:30 is
At 3:40, the hour and minute hands of a clock are inclined at
If OP makes 4 revolutions in one second, the angular velocity in radians per second is
A circular wire of radius 3 cm is cut and bent so as to lie along the circumference of a hoop whose radius is 48 cm. Find the angle in degrees which is subtended at the centre of hoop.
Find the value of `sqrt(3)` cosec 20° – sec 20°
State whether the statement is True or False? Also give justification.
The equality sinA + sin2A + sin3A = 3 holds for some real value of A.
State whether the statement is True or False? Also give justification.
One value of θ which satisfies the equation sin4θ - 2sin2θ - 1 lies between 0 and 2π.
