Ratio of Sides of Special Triangles

Q.

A tower is 60 m high. Its shadow is x metres shorter when the sun’s altitude is 45° instead of 30°. Then, x is equal to:

1. 43 m

2. 41.92 m

3. 45.6 m

4. 43.92 m

Q.

In a triangle $ABC$ right angled at $B$, if $\tan \left(A\right)=\frac{1}{\sqrt{3}}$ find the value of $\sin \left(\mathrm{A}\right)\cos \left(\mathrm{C}\right)+\sin \left(\mathrm{C}\right)\cos \left(\mathrm{A}\right)$.

Q.

In $\Delta ABC,\angle A={40}^{\circ },BC=8cm.$ Find the circumdiameter of the triangle. $[sin{40}^{\circ }=0.64]$

1. 14 cm

2. 10.5 cm

3. 15 cm

4. 12.5 cm

Q.

In $\Delta ABC,AB=10cm,AC=6cm,\angle A={70}^{\circ }$. Find the length of the side BC. $[cos{70}^{\circ }=0.34,sin{70}^{\circ }=0.94]$

Q.

What is sin $\theta$ in the given right triangle, right angled at B?

1. $\frac{3}{5}$

2. $\frac{5}{3}$

3. $\frac{4}{5}$

4. $\frac{3}{4}$

Q.

In a triangle $ABC$, if $\cos A+\cos B+\cos C=7/4$, then $\frac{R}{r}$ is equal to

1. $\frac{4}{7}$

2. $\frac{4}{3}$

3. $\frac{3}{4}$

4. None of the above

Q. A boy is looking at the top of a building which is 10 m high.
From the figure, the distance between the boy and the building will be .

1. 10 m
2. 20 m
3. 5 m
4. 25 m

Q.

In $\Delta ABC,\angle A={60}^{\circ },BC=10cm.$ The circumdiameter of the triangle is $[sin{60}^{\circ }=0.87]$

1. 12.11 cm

2. 14.97 cm

3. 11.49 cm

4. 13.45 cm

Q.

What is the value of sin $\theta$ for the given right triangle, right angled at B?

1. 3/5

2. 5/3

3. 4/5

4. 3/4

Q.

What is sin $\theta$ in the given right triangle, right angled at B?

1. 5/3

2. 4/5

3. 3/4

4. 3/5

Q.

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

Q.

In $\Delta ABC,\angle A={50}^{\circ },BC=8cm.$ Find the circumdiameter of the triangle $[sin{50}^{\circ }=0.77]$

1. 12.54 cm

2. 10.38 cm

3. 11.4 cm

4. 9.8 cm

Q.

In triangle $ABC,\angle A={130}^{\circ },BC=10cm$. The diameter of the circumcircle is $[sin{50}^{\circ }=0.76]$

1. 10.5 cm

2. 13.15 cm

3. 15.25 cm

4. 14.75 cm

Q.

If $|u|<1,|v|<1$, and $z=\frac{u-v}{1+\overline{u}v}$, then least value of $|z|$ is

1. $\frac{|u|-|v|}{1+|u||v|}$

2. $\frac{||u|-|v||}{1-|u||v|}$

3. $\frac{|u|+|v|}{1+|u||v|}$

4. None of these

Q.

What is sin $\theta$ in the given right triangle, right angled at B?

1. $\frac{3}{5}$

2. $\frac{5}{3}$

3. $\frac{4}{5}$

4. $\frac{3}{4}$

Q.

What is the value sin $\theta$ in the given right triangle, right angled at B?

1. 3/5

2. 5/3

3. 4/5

4. 3/4

Q. In a right angled triangle, the ratio of sin $\theta$ is given by the opposite side to the hypotenuse.

1. True
2. False

Q.

In $\Delta ABC,\angle A={60}^{\circ },BC=10cm.$ Find the circumdiameter of the triangle. $[sin{60}^{\circ }=0.87]$

Q.

If a triangle has angles ${45}^{\circ },{45}^{\circ }$, and ${90}^{\circ }$, what is the ratio of the sides of the triangle opposite to these angles respectively?

1. $1:1:\sqrt{2}$
2. $\sqrt{3}:2:1$
3. $\sqrt{2}:1:1$
4. $1:2:\sqrt{3}$

Q.

A ladder is placed along a wall such that its upper end is resting against a vertical wall. The foot of the ladder is 20 m from the wall and the ladder is making an angle of ${60}^{\circ }$ with the ground. Find the height, upto which the ladder reaches. [2 MARKS]

Q. If $\tan \theta =\frac{4}{3}$, what is the value of $\cos \theta$?

1. 0.6

Q. In a $△ABC,\angle A={60}^{\circ },\angle B={30}^{\circ }and\angle C={90}^{\circ }.$

Then the ratio AC:BC:AB will be equal to ___.

1. $1:2:\sqrt{3}$
2. $1:1:\sqrt{2}$
3. $1:\sqrt{3}:2$
4. $\sqrt{3}:2:1$

Q. In the given right triangle, the value of $\sin \theta$ is .

1. $\frac{3}{5}$
2. $\frac{5}{3}$
3. $\frac{4}{5}$
4. $\frac{3}{4}$

Q.

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

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

Q. In the figure, the $\angle ABC=30°$. If $CB=18m$ , then AC = ________.

1. $9\sqrt{3}m$
2. $9m$
3. $3m$
4. $3\sqrt{3}m$

Q. In the given right triangle, the value of $\sin \theta$ is .

1. $\frac{3}{5}$
2. $\frac{5}{3}$
3. $\frac{4}{5}$
4. $\frac{3}{4}$

Q. Find angle ${}^{\prime }{A}^{\prime }$ in degrees from the above figure :

Q.

What is sin $\theta$ in the given right triangle, right angled at B?

1. 3/5

2. 5/3

3. 4/5

4. 3/4

Q.

Two poles are erected from the ground. The length of the longer pole is 10m. If the distance between the tips of the poles is 6m, and the angle of elevation of the tip of the longer pole from that of the shorter pole is ${30}^{\circ }$, find the length of the second pole.

Q. In a right angled triangle, the ratio of sin $\theta$ is given by the opposite side to the hypotenuse.

1. True
2. False