मराठी

In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord.

Advertisements
Advertisements

प्रश्न

In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord.

बेरीज
Advertisements

उत्तर

Triangle OAB is an equilateral triangle ∠AOB = 60°

= `(60×π)/180 "radians"`

= `π/3` radian

Let arc AB = l

The angle made by the arc at centre O, θ = `π/3` Length of arc AB,

l = rθ = 20 × `π/3` radians

= `(20π)/3` radians

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 3: Trigonometric Functions - EXERCISE 3.1 [पृष्ठ ४९]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 11
पाठ 3 Trigonometric Functions
EXERCISE 3.1 | Q 5. | पृष्ठ ४९

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Find the radian measure corresponding to the following degree measure:

520°


Find the degree measure corresponding to the following radian measure (Use `pi = 22/7`)

-4


Find the degree measures corresponding to the following radian measures (Use `pi = 22/7`)

`(5pi)/3`


A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?


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

21 cm


Find the degree measure corresponding to the following radian measure:
\[\frac{9\pi}{5}\]


Find the degree measure corresponding to the following radian measure: 
(−3)c


Find the degree measure corresponding to the following radian measure: 
 11c


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 pentagon.


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

\[60^\circ, 80^\circ, 100^\circ\text{ and }120^\circ\], respectively.
Angles of the quadrilateral in radians =
\[\left( 60 \times \frac{\pi}{180} \right), \left( 80 \times \frac{\pi}{180} \right) , \left( 100 \times \frac{\pi}{180} \right) \text{ and }\left( 120 \times \frac{\pi}{180} \right)\]
\[\frac{\pi}{3}, \frac{4\pi}{9}, \frac{5\pi}{9}\text{ and } \frac{2\pi}{3}\]
 

 


The angle in one regular polygon is to that in another as 3 : 2 and the number of sides in first is twice that in the second. Determine the number of sides of two polygons.

 

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 wheel makes 360 revolutions per minute. Through how many radians does it turn in 1 second?

 

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?

 

If the angles of a triangle are in A.P., then the measures of one of the angles in radians 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


The radius of the circle whose arc of length 15 π cm makes an angle of \[\frac{3\pi}{4}\]  radian 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 value of tan1° tan2° tan3° ... tan89° is ______.


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.

Sin10° is greater than cos10°


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.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×