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. - Mathematics

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:

25°


Find the radian measure corresponding to the following degree measure:

240°


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)`

`11/16`


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

`(7pi)/6`


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


Find the degree measure corresponding to the following radian measure: 
 1c


Find the radian measure corresponding to the following degree measure: −56°


Find the radian measure corresponding to the following degree measure: 125° 30'


The difference between the two acute angles of a right-angled triangle is \[\frac{2\pi}{5}\] radians. Express the angles in degrees.

 

 


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.


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 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.

 

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?

 

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 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


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 `sqrt(3)` cosec 20° – sec 20°


If θ lies in the second quadrant, then show that `sqrt((1 - sin theta)/(1 + sin theta)) + sqrt((1 + sin theta)/(1 - sin theta))` = −2sec θ


Prove that `(sec8 theta - 1)/(sec4 theta - 1) = (tan8 theta)/(tan2 theta)`


If tan θ = `(-4)/3`, then sin θ is ______.


The value of tan1° tan2° tan3° ... tan89° is ______.


The value of cos1° cos2° cos3° ... cos179° is ______.


Which of the following is correct?

[Hint: 1 radian = `180^circ/pi = 57^circ30^'` approx]


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.

`cos  (2pi)/15 cos  (4pi)/15 cos  (8pi)/15 cos  (16pi)/15 = 1/16`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×