मराठी

Find the Length Which at a Distance of 5280 M Will Subtend an Angle of 1' at the Eye.

Advertisements
Advertisements

प्रश्न

Find the length which at a distance of 5280 m will subtend an angle of 1' at the eye.

 
Advertisements

उत्तर

We have:
Radius = 5280 m
Now,
\[\theta = 1' = \left( \frac{1}{60} \right)^\circ = \left( \frac{1}{60} \times \frac{\pi}{180} \right)\text{ radian }\]
We know:

\[\theta = \frac{\text{ Arc }}{\text{ Radius }}\]
\[ \Rightarrow \frac{1}{60} \times \frac{\pi}{180} = \frac{\text{  Arc }}{5280}\]
\[ \Rightarrow \text{ Arc }= \frac{5280 \times 22}{60 \times 180 \times 7} = 1 . 5365 m\]
shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 4: Measurement of Angles - Exercise 4.1 [पृष्ठ १५]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
पाठ 4 Measurement of Angles
Exercise 4.1 | Q 12 | पृष्ठ १५

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Find the radian measure corresponding to the following degree measure:

– 47° 30'


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

`(5pi)/3`


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`)


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


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

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:
\[\left( \frac{18\pi}{5} \right)\]


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


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: 135°


Find the radian measure corresponding to the following degree measure: 7° 30'


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

 

 


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. such that the greatest is 5 times the least. 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?

 

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

 

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.

 

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


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

 

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.


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 ______.


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°


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×