Sine Rule

Q.

The angles $A,B,C$ of a triangle $ABC$ are in $A.P$ and $a:b=1:\sqrt{3}$ . If $c=4cm$, then the area (in $sq.cm$) of this triangle is

Q.
Find the length of side AC.

1. $sin\theta$
2. $\frac{sin\theta }{\sqrt{3}}$
3. $\sqrt{3}sin\theta$
4. $\sqrt{3}{sin}^2\theta$

Q.

The parallel sides of an isosceles trapezium are 10cm and 6cm respectively and one of the non-parallel sides is 8cm. If the angle between the non-parallel and parallel side is ${110}^{\circ }$, then the area of the trapezium is ___ $[sin{70}^{\circ }=0.93]$

1. $55c{m}^2$

2. $70c{m}^2$

3. $50c{m}^2$

4. $60.08c{m}^2$

Q.

In $\Delta ABC,\angle A={50}^{\circ },\angle B={70}^{\circ },AB=6cm.$ The length of 2 sides BC and AC are $[sin{50}^{\circ }=0.77,sin{60}^{\circ }=0.87sin{70}^{\circ }=0.94]$

1. 6.2 cm, 7.5 cm

2. 5.313 cm, 6.486 cm

3. 5.1 cm, 4.9 cm

4. 5.9 cm, 7.2 cm

Q.

In the given figure triangle ABC is circumscribed in a circle of radius 10 cm. The value of $\frac{AB}{sinC}$ is equal to

1. 20 cm

2. 10 cm

3. 40 cm

4. $20\sqrt{2}cm$

Q.

A circle of radius R is circumscribing a triangle ABC, having $\angle A={30}^{\circ }$, & BC = 20 cm. Then the radius 'R' is equal to $[sin{30}^{\circ }=0.5]$

1. 20 cm

2. 10 cm

3. 40 cm

4. $20\sqrt{3}cm$

Q.

In triangle ABC, $\angle CAB={40}^{\circ }$, AC = 6 cm, AB = 7 cm. The length BC is equal to_____. $[sin{40}^{\circ }=0.67,cos{40}^{\circ }=0.76]$

1. 6.55 m

2. 4.55 m

3. 5.65 m

4. 7.25 m

Q.

$\sin 65°\cos 38°=$

Q. In a circle, the length of any chord is double the product of the and the sine of half of the .

1. central angle
2. radius
3. diameter
4. secant

Q.

The parallel sides of an isosceles trapezium are 12 cm and 8 cm respectively and the non-parallel side measures 10 cm and makes an angle of ${120}^{\circ }$ with the parallel side. Then the distance between the parallel sides is $[sin{60}^{\circ }=0.86]$

1. 7.5 cm

2. 8.6 cm

3. 9.5 cm

4. 10.6 cm

Q.

In the given figure, a circle is circumscribing $\Delta ABC$ where $\angle A={125}^{\circ }$ and side BC=8cm. The diameter of the circumcircle is equal to

$[sin{55}^{\circ }=0.82]$

1. 12.5 cm

2. 10.75 cm

3. 9.75 cm

4. 8.25 cm

Q.

In the given figure triangle ABC is circumscribed by a circle, AB =5 cm, $\angle A={30}^{\circ },\angle C={60}^{\circ }$.The length BC equal is to $[sin{60}^{\circ }=0.86,sin{30}^{\circ }=0.5]$

1. 2.9 cm

2. 4 cm

3. 2.1 cm

4. 3.5 cm

Q.

In a triangle ABC, AB =20 cm, $\angle A={30}^{\circ }$, AC = 18 cm. Find the area of the triangle

Q. A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is ${60}^{\circ }$. After some time, the angle of elevation reduces to ${30}^{\circ }$. Find the distance travelled by the balloon during the interval.

Q.

In the given triangle $ABC,\angle A={50}^{\circ },\angle c={50}^{\circ }$, AB =10 cm, then find the length of BC. $[sin{60}^{\circ }=0.86,sin{50}^{\circ }=0.76]$

Q.
If $sinA=\frac{1}{2}$, then find the value of cot A.

Q.

A tree 12 m high, is broken by the wind in such a way that its top touches the ground and makes an angle ${60}^{\circ }$ with the ground. At what height from the bottom the tree is broken by the wind? [3 MARKS]

Q. A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is ${60}^{\circ }$. After some time, the angle of elevation reduces to ${30}^{\circ }$. Find the distance travelled by the balloon during the interval.

Q. If A is an acute angle and tan A + cot A = 2 then find the value of tan^9 A + cot^7 A.

Q. Prove that: $co{s}^{2}A+co{s}^{2}B-co{s}^{2}C=1-2sinA.SinB.cosC$

Q.

In the given figure triangle ABC is circumscribed by a circle, AB =5 cm, $\angle A={30}^{\circ },\angle C={60}^{\circ }$. Find the length of side BC. $[sin{60}^{\circ }=0.86,sin{30}^{\circ }=0.5]$

Q.

Two sides of a triangle are 8cm and 12cm, and the angle between them is ${110}^{\circ }$ as shown in the figure.

Area of the triangle is ___ ($sin{70}^{\circ }=0.93$)

1. $45.5c{m}^2$

2. $37.58c{m}^2$

3. $54.81c{m}^2$

4. $48.5c{m}^2$

Q.

In the given triangle $ABC,\angle A={50}^{\circ },\angle c={50}^{\circ }$, AB =10 cm, then BC is equal to $[sin{60}^{\circ }=0.86,sin{50}^{\circ }=0.76]$

1. 12.8 cm

2. 11.31 cm

3. 13.4 cm

4. 14.8 cm

Q.

In $\Delta ABC,AB=10cm,AC=6cm,\angle A={70}^{\circ }$. The length BC is equal to. $[cos{70}^{\circ }=0.34,sin{70}^{\circ }=0.94]$

1. 9.75 cm

2. 7.5 cm

3. 10.5 cm

4. 8.25 cm

Q. Prove :$\frac{\sin A}{1+\cos A}+\frac{1+\cos A}{\sin A}=2cosecA.$

Q. The meaning of $Sin2A$ and $2SinA$ is different.

1. True
2. False

Q.

We can cut out a triangle whose one side is 7cm and the angle opposite to this side is ${40}^{\circ }$ from a circular sheet of diameter 10cm.

$[sin{40}^{\circ }=0.64]$

1. True

2. False

Q. If A, B and C are interior angles of a triangle ABC, and
$\sin \left(\frac{B+C}{2}\right)=\cos \left(x\right),$
then what is the value of x?

Q. In the given figure , O is the centre of the circle and $TP$ is the tangent to the circle from an external point $T$. If $\angle PBT={30}^o$, prove that $BA:AT=2:1$?

Q.

In $\Delta ABC$, $\angle C={30}^{\circ },\angle B={80}^{\circ },\angle A={70}^{\circ },AB=12cm$ as shown in the figure. The length of the side AC is equal to ___

$\left[\begin{array}{c}sin{30}^{\circ }=0.5\\ sin{70}^{\circ }=0.93\\ sin{80}^{\circ }=0.98\end{array}\right]$

1. 20.95 cm

2. 21.8 cm

3. 23.63 cm

4. 26.8 cm