Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Let AB be the chord and O be the centre of the circle.
Here,
AO = BO = AB = 30 cm
Therefore,
∆ AOB is an equilateral triangle .
Now,
Radius = 30 cm
\[\theta = 60^\circ = \left( 60 \times \frac{\pi}{180} \right) = \frac{\pi}{3}\text{ radian }\]
\[ \Rightarrow \frac{\pi}{3} = \frac{\text{Arc}}{30}\]
\[ \Rightarrow \text{Arc} = \frac{30\pi}{3} = 10\pi cm\]
APPEARS IN
संबंधित प्रश्न
Find the radian measure corresponding to the following degree measure:
25°
Find the degree measure corresponding to the following radian measure `(use pi = 22/7)`
`11/16`
Find the degree measures corresponding to the following radian measures (Use `pi = 22/7`)
`(5pi)/3`
If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their radii.
Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length
10 cm
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 angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length
21 cm
Find the degree measure corresponding to the following radian measure:
1c
Find the radian measure corresponding to the following degree measure: −300°
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 pentagon.
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. and the number of degrees in the least angle is to the number of degrees in the mean angle as 1 : 120. Find the angles in radians.
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.
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 D, G and R denote respectively the number of degrees, grades and radians in an angle, the
If the angles of a triangle are in A.P., then the measures of one of the angles in radians is
At 3:40, the hour and minute hands of a clock are inclined at
If the arcs of the same length in two circles subtend angles 65° and 110° at the centre, than the ratio of the radii of the circles is
If OP makes 4 revolutions in one second, the angular velocity in radians per second is
A circular wire of radius 7 cm is cut and bent again into an arc of a circle of radius 12 cm. The angle subtended by the arc at the centre is
Find the value of tan 9° – tan 27° – tan 63° + tan 81°
Prove that `(sec8 theta - 1)/(sec4 theta - 1) = (tan8 theta)/(tan2 theta)`
“The inequality `2^sintheta + 2^costheta ≥ 2^(1/sqrt(2))` holds for all real values of θ”
The value of cos1° cos2° cos3° ... cos179° is ______.
State whether the statement is True or False? Also give justification.
Sin10° is greater than cos10°
