PAGE-4.11
Exercise 4.1
Question 1
Find the degree measure corresponding to the following radian measures :
(i) $\left(\frac{4 \pi}{3}\right)^{c}$
Sol :
$1^{c}=\left\{\frac{180^{\circ}}{\pi}\right\}$
Now, $\frac{4 \pi}{3} \times \frac{180^{\circ}}{\pi}$
=4×60=240°
(ii) $\left(\frac{7 \pi}{6}\right)^{c}$
Sol :
$=\frac{7 \pi}{6} \times \frac{180^{\circ}}{\pi}$
=7×30=210°
(iii) $\left(\frac{5 \pi}{3}\right)^{c}$
Sol :
$=\frac{5 \pi}{3} \times \frac{180^{\circ}}{\pi}$
=5×60=300°
(iv) $\left(-\frac{5 \pi}{24}\right)^{c}$
Sol :
$=-\frac{5 \pi}{24} \times \frac{180^{\circ}}{\pi}$
$=-\frac{5}{2} \times 15^{\circ}=\frac{-75^{\circ}}{2}$
=-37.5°
∴1°=60'
(0.5×60)'=30'
=-37° 30'
(v) $\left(-\frac{2 \pi}{3}\right)^{c}$
Sol :
$=-\frac{2 \pi}{3} \times \frac{180^{\circ}}{\pi}$
=-2×60=-120°
(vi) $\left(\frac{33 \pi}{320}\right)^{c}$
Sol :
(vii) $6^{c}$
Sol :
(viii) $(-4)^{c}$
Sol :
(ix) $\left(\frac{11}{16}\right)^{c}$
Sol :
(x) $(2.64)^{c}$
Sol :
Question 2
Express the following angles in radian measure
(i) 105°
(ii) 25°
(iii) 240°
(iv) -56°
(v) 520°
(vi) $7^{\circ} 30^{\prime}$
(vii) $40^{\circ} 20^{\prime}$
(viii) $42^{\circ} 57^{\prime} 16^{\prime \prime}$
(ix) $-47^{\circ} 30^{\prime}$
Question 3
Two angles of a triangle are $72^{\circ} 53^{\prime} 51^{\prime \prime}$ and $41^{\circ} 22^{\prime} 50^{\prime \prime}$ respectively. Find the third angle in radians.
Sol :
Question 4
Find the angle between the hour-hand and minute-hand in circular measure at 4 O'clock.
Sol :
Question 5
The angles of a triangle are in A.P. and the number of degrees in the least is to the number of radians in the greatest is 36 : 𝝿, find the angles in degrees.
Sol :
TYPE-II
Question 6
Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length $22 \mathrm{~cm}\left(\right.$ use $\left.\pi=\frac{22}{7}\right)$.
Sol :
Question 7
(i) Find the radius of the circle in which a central angle of 45° makes an arc of 187 cm $\left(\right.$ use $\left.\pi=\frac{22}{7}\right)$
(ii) Find the radius of the circle in which a central angle of $60^{\circ}$ intercepts an arc of length 37.4 cm use $\left.\pi=\frac{22}{7}\right)$.
Sol :
Question 8
In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor are of the chord.
Sol :
Question 9
At what distance does a man $5 \frac{1}{2} \mathrm{ft}$ in height, subtend an angle of $15^{\prime \prime}$ ?
Sol :
Question 10
In two circles, arcs of equal length subtend angles of 60° and 75° at their centres. show that their radii are in the ratio 5: 4
Question 11
(i) If the arcs of same length in two circles subtend angles of $75^{\circ}$ and 120 at their respective centres, find the ratio of their radii.
(ii) If arcs of the same lengths in two circles subtend angles of $65^{\circ}$ and 110 at the centre, find the ratio of their radii.
Sol :
Question 12
Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an are of length :
(i) 10 cm
(ii) 21 cm
(iii) 15 cm $\left(\right.$ use $\left.\pi=\frac{22}{7}\right)$
Question 13
The minute hand of a watch is 1.5 cm long. How far does its tip move in
(i) 50 minutes (ii) 40 minutes ? (use $\pi=3.14$ )
Question 14
(i) A wheel makes 30 revolutions per minute. Find the radian measure of the angle described by one of the spokes of the wheel in $\frac{1}{2}$ second.
(ii) A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?
Sol :
Question 15
Assuming the average distance of the earth from the sun to be 149700000 km and the angle subtended by the sun at the eye of a person on the earth to be $32^{\prime}$. find the sun's diameter.
Question 16
A truck is travelling on a circular road of radius 1500 metres at 66 km/hr. Through what angle (in radians) does it turn in 10 seconds ?
Question 17
If the angular diameter of the moon be 30', how far from the eye should a coin of diameter 2.2 cm be kept to hide the moon ?
Sol :
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