CDS QUANT TRIGONOMETRY QUIZ 27

Question 1:

In a triangle $A B C, A B=20 \mathrm{~cm}, \angle A B C=30^{\circ}$ and $\angle A C B=45^{\circ}$, Find the area of the triangle.

$150(\sqrt{3}+1)$

$200(\sqrt{3}+1)$

$50(3+\sqrt{3})$

$50(\sqrt{3}+1)$

Question 2:

Two sides of triangle is $10 \mathrm{~cm}$ and $20 \mathrm{~cm}$ area is $80 \mathrm{~cm}^{2}$. Find the third side.

$\sqrt{65}$

$2 \sqrt{65}$

$\frac{1}{2} \sqrt{65}$

12

Question 3:

If in a triangle $\Delta \mathrm{ABC}, \operatorname{acos}^{2}\left(\frac{C}{2}\right)+\operatorname{ccos}^{2}\left(\frac{A}{2}\right)$

$=\frac{3 b}{2}$, then the side's a, b and c are.

satisfy $a+b=c$

A.P

G.P

H.P

Question 4:

In a triangle $\mathrm{ABC}, 2 \mathrm{ac} \sin \frac{1}{2}(\mathrm{~A}-\mathrm{B}+\mathrm{C})=$

$a^{2}+b^{2}-c^{2}$

$c^{2}-a^{2}-b^{2}$

$b^{2}+c^{2}-a^{2}$

$c^{2}+a^{2}-b^{2}$

Question 5:

In the given figure, find the area?

$\frac{135 \sqrt{3}}{4}$

$\frac{145 \sqrt{3}}{4}$

$\frac{120 \sqrt{3}}{7}$

$\frac{145 \sqrt{5}}{7}$

Question 6:

If the lengths of the sides of a triangle are in A.P. and the greatest angle is double the smallest, then a ratio of lengths of sides of a triangle is.

$4: 5: 6$

$3: 4: 5$

$5: 9: 13$

$5: 6: 7$

Question 7:

In the given figure, if $\mathrm{AB}=\mathrm{AC}=8 \mathrm{~cm}, \mathrm{BC}=$ $11 \mathrm{~cm}$ and $\mathrm{BD}=7 \mathrm{~cm}$, then find $\mathrm{AD}=$ ?

$6 \mathrm{~cm}$

$5.5 \mathrm{~cm}$

$4 \mathrm{~cm}$

$7 \mathrm{~cm}$

Question 8:

The side of triangle are $3 x+4 y, 4 x+3 y$ and $5 x+5 y$ Where $x, y>0$ then the triangle is:

Right angled

Obtuse angled

Acute angled

Equilateral

Question 9:

In a $\triangle \mathrm{ABC}, \mathrm{AD}$ divides $\mathrm{BC}$ in the ratio $2: 3$, $\angle \mathrm{B}=30^{\circ}, \angle \mathrm{C}=45^{\circ} .$ Find $\frac{\sin \angle \mathrm{BAD}}{\sin \angle \mathrm{CAD}} .$

$\frac{\sqrt{3}}{2}$

$\frac{\sqrt{2}}{3}$

$\frac{2}{\sqrt{3}}$

$\frac{1}{\sqrt{3}}$

Question 10:

In a triangle $\mathrm{ABC}, \angle \mathrm{A}=30^{\circ}, \angle \mathrm{C}=90^{\circ}$, Find the ratio of side?

$1: \sqrt{3}: 2$

$1: 2: \sqrt{3}$

$\sqrt{3}: 2: 1$

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