CDS TRIGONOMETRY QUIZ 28

Question 1:

In a triangle $\mathrm{ABC}, \mathrm{AC}=8 \mathrm{~cm}, \mathrm{AB}=6 \mathrm{~cm}$, and $\mathrm{BC}=12 \mathrm{~cm}$ then find the value of $\angle \mathrm{ACB}$ $=?$

$\cos ^{-1}\left(\frac{43}{48}\right)$

$\cos ^{-1}\left(\frac{47}{51}\right)$

$\cos ^{-1}\left(\frac{41}{59}\right)$

$\cos ^{-1}\left(\frac{49}{53}\right)$

Question 2:

In a triangle $A B C$, if $(a+b+c)(a-b+c)=$ 3ac, then find $\angle B=$ ?

$45^{\circ}$

$60^{\circ}$

$30^{\circ}$

$90^{\circ}$

Question 3:

The sides of the triangle are $\sin \alpha, \cos \alpha$ and $\sqrt{(1+\sin \alpha \cos \alpha)}$ for some $0<\alpha<\frac{\pi}{2}$, then find the greatest angle of the triangle is.

$150^{\circ}$

$90^{\circ}$

$120^{\circ}$

$60^{\circ}$

Question 4:

In a triangle $\mathrm{ABC}, \mathrm{AC}=8 \mathrm{~cm}, \mathrm{BC}=6 \mathrm{~cm}$ and $\angle \mathrm{C}=30^{\circ}$ then find the value of $\mathrm{AB}=$ ?

$5.2 \mathrm{~cm}$

$4.1 \mathrm{~cm}$

$3.25 \mathrm{~cm}$

$6.25 \mathrm{~cm}$

Question 5:

In a triangle $\mathrm{ABC}, \mathrm{AC}=10 \mathrm{~cm}, \mathrm{BC}=x \mathrm{~cm}$ and $\angle \mathrm{C}=60^{\circ}, \angle \mathrm{B}=45^{\circ}$ then find the value of $x$.

$10 \mathrm{~cm}$

$15.26 \mathrm{~cm}$

$12.24 \mathrm{~cm}$

$8.42 \mathrm{~cm}$

Question 6:

In a $\Delta \mathrm{ABC}$, if $\mathrm{a}^{2}, \mathrm{~b}^{2}, \mathrm{c}^{2}$ are in A.P, then find $\cot A, \cot B, \cot C$ are in $\ldots . . .$

A.P

G.P

H.P.

None of these.

Question 7:

Two sides of a triangle are given by the roots of equation $x^{2}-2 \sqrt{3} x+2=0$ and the angle between the sides is $\frac{\pi}{3}$. Then find the perimeter of the triangle.

$2 \sqrt{3}$ units

$\sqrt{6}$ units

$(2 \sqrt{3}+\sqrt{6})$ units

$2(\sqrt{3}+\sqrt{6})$ units

Question 8:

In a triangle $\mathrm{ABC}, \mathrm{AC}=20 \mathrm{~cm}, \mathrm{BC}=10 \mathrm{~cm}$ and $\angle B=60^{\circ}$, then find the value of $\angle A$.

$\sin ^{-1}\left(\frac{\sqrt{3}}{8}\right)$

$\sin ^{-1}\left(\frac{\sqrt{5}}{6}\right)$

$\sin ^{-1}\left(\frac{\sqrt{3}}{4}\right)$

None of these.

Question 9:

The perimeter of a triangle $\mathrm{ABC}$ is 6 times the arithmetic mean of the sines of its angles. If the side a is 1 , then find angle $\mathrm{A}$.

$\frac{\pi}{3}$

$\frac{2 \pi}{3}$

$\frac{\pi}{6}$

$\frac{\pi}{4}$

Question 10:

If the lengths of the sides of triangles are 3 ,5,7 then the largest angle of the triangle is.

$\frac{\pi}{2}$

$\frac{5 \pi}{4}$

$\frac{3 \pi}{4}$