SSC CHSL (TRIGONOMETRY) QUANT QUIZ

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Question 1:

If $\cot B=\frac{12}{5}$, what is the value of $\sec B$ ?

Question 2:

A vertical pole and a vertical tower are on the same level ground in such a way that, from the top of the pole, the angle of elevation of the top of the tower is $60^{\circ}$ and the angle of depression of the bottom of the tower is $30^{\circ}$. If the height of the pole is $24 \mathrm{~m}$, then find the height of the tower (in $\mathrm{m}$ ).

Question 3:

The angle of elevation of the top of a tall building from the points M and N at the distances of 72 m and 128 m, respectively, from the base of the building and in the same straight line with it, are complementary. The height of the building (in m) is:

Question 4:

If $2 k \sin 30^{\circ} \cos 30^{\circ} \cot 60^{\circ}=\frac{\cot ^2 30^{\circ} \sec 60^{\circ} \tan 45^{\circ}}{\operatorname{cosec}^2 45^{\circ} \operatorname{cosec} 30^{\circ}}$, then find the value of $k$

Question 5:

A vertical pole and a vertical tower are placed on a flat ground such that the angle of elevation of the top of the tower from the top of the pole is $60^{\circ}$ and the angle of depression of the base of the tower  from the top of the pole is $30^{\circ}$. If the height of the tower is $76 \mathrm{~m}$, then find the height of the pole (in $\mathrm{m}$).

Question 6:

If $\cos (A-B)=\frac{\sqrt{3}}{2}$ and $\sec A=2,0^{\circ} \leq A \leq 90^{\circ}, 0^{\circ} \leq B \leq 90^{\circ}$, then what is the measure of B?

Question 7:

What is the value of:

$8 \sqrt{3} \sin 30^{\circ} \tan 60^{\circ}-3 \cos 0^{\circ}+3 \sin ^{2} 45^{\circ}+2 \cos ^{2} 30 ?$

Question 8:

From the top of a platform 7m high, the angle of elevation of a tower $30^{\circ}$. If the tower was 47 m high, how far away from the tower was the platform positioned? 


Question 9:

The tops of two poles of heights $18 \mathrm{~m}$ and $30.5 \mathrm{~m}$ are connected by a wire. If the wire makes an angle of $30^{\circ}$ with the horizontal, what is the length (in $\mathrm{m}$ ) of the wire?

Question 10:

If $6 \tan A(\tan A+1)=5-\tan A$, Given that $0 < A <\frac{\pi}{2}$ what is the value of $(\sin A+\cos A) ?$