Sexagesimal System

Q.

Find the value of $\tan {75}^0$.

Q.

Prove that $\tan 50°-\tan 40°=2\tan 10°$

Q. $85.12°\mathrm{in}\mathrm{degree}\mathrm{decimal}\mathrm{system}\mathrm{can}\mathrm{be}\mathrm{expressed}\mathrm{in}\mathrm{sexagesimal}\mathrm{system}\mathrm{as}:$

1. $85°715$
2. $85°712$
3. $85°815$
4. $85°812$

Q.

If $\angle C=90°$ in the triangle ABC, then ${\tan }^{-1}\left(\frac{b}{b+c}\right)+{\tan }^{-1}\left(\frac{b}{c+a}\right)=$

1. $\frac{\mathrm{\pi }}{2}$

2. $\frac{\mathrm{\pi }}{4}$

3. $\frac{\mathrm{\pi }}{3}$

4. $\mathrm{\pi }$

Q. A wheel makes 12 revolutions per hour The radians it turns through in 20 minutes is:

1. $8{\pi }^c$
2. $16{\pi }^c$
3. $32{\pi }^c$
4. $24{\pi }^c$

Q. If the length of tangents from $A,B,C$ to the incircle of $\Delta ABC$ are $4,6,8$ then which of the following is/are correct:

1. Area of $\Delta ABC$ is $12\sqrt{6}$
2. $r_1,r_2,r_3$ are in $HP$
3. $a,b,c$are in $AP$
4. $r=\frac{4\sqrt{6}}{3}$

Q.

From given figure, $\sin x+\sec x+\tan x$ is $\alpha$, find $156\alpha$.

__

Q. $85.12°\mathrm{in}\mathrm{degree}\mathrm{decimal}\mathrm{system}\mathrm{can}\mathrm{be}\mathrm{expressed}\mathrm{in}\mathrm{sexagesimal}\mathrm{system}\mathrm{as}:$

1. $85°7\text{'}12\text{'}\text{'}$
2. $85°8\text{'}12\text{'}\text{'}$
3. $85°7\text{'}15\text{'}\text{'}$
4. $85°8\text{'}15\text{'}\text{'}$

Q.

If an angle $\alpha$ is divided into two parts $A\mathrm{and}B$ such that $A–B=x$ and $\tan A:\tan B=2:1$, then what is $\sin x$ equal:

1. $3\sin \alpha$

2. $\frac{2\sin \alpha }{3}$

3. $\frac{\sin \alpha }{3}$

4. $2\sin \alpha$

Q. ${127.83}^{\circ }$ is equivalent to

1. ${127}^{\circ }{47}^{\prime }{48}^{\prime \prime }$
2. ${127}^{\circ }{49}^{\prime }{18}^{\prime \prime }$
3. ${127}^{\circ }{45}^{\prime }{48}^{\prime \prime }$
4. ${127}^{\circ }{49}^{\prime }{48}^{\prime \prime }$

Q. ${35.47}^{\circ }$ is equivalent to

1. ${35}^{\circ }{28}^{\prime }{18}^{\prime \prime }$
2. ${35}^{\circ }{28}^{\prime }{12}^{\prime \prime }$
3. ${35}^{\circ }{24}^{\prime }{12}^{\prime \prime }$
4. ${35}^{\circ }{28}^{\prime }{16}^{\prime \prime }$

Q. The ratio of angles in one regular polygon to that in another is $3:2$. The number of sides in the first is twice the second. How many sides do the second polygon have?

Q. ${127.83}^{\circ }$ is equivalent to

1. ${127}^{\circ }{47}^{\prime }{48}^{\prime \prime }$
2. ${127}^{\circ }{49}^{\prime }{18}^{\prime \prime }$
3. ${127}^{\circ }{49}^{\prime }{48}^{\prime \prime }$
4. ${127}^{\circ }{45}^{\prime }{48}^{\prime \prime }$

Q. 1800" in sexagesimal system is equal to ​​​​​degrees in decimal degree system.

Q.

	A	A	B	B	C	C	D	D	E	E
	M	S	M	S	M	S	M	S	M	S
$2006$	$2.8$	$1.3$	$3.3$	$2.2$	$2.6$	$1.7$	$3.0$	$2.2$	$1.9$	$1.4$
$2007$	$3.2$	$2.0$	$2.4$	$1.6$	$2.2$	$1.5$	$2.5$	$1.9$	$2.0$	$1.7$
$2008$	$1.9$	$0.9$	$2.9$	$1.6$	$2.1$	$1.0$	$2.3$	$1.5$	$1.6$	$1.1$
$2009$	$1.0$	$0.4$	$2.4$	$1.3$	$2.8$	$1.4$	$2.1$	$1.2$	$3.2$	$2.5$
$2010$	$2.5$	$1.5$	$2.3$	$1.2$	$2.6$	$2.1$	$1.8$	$1.1$	$3.1$	$2.6$

What is the total number of units manufactured by company C over all the years together?

1. $10.30$
2. $14.20$
3. $13.20$
4. $12.30$

Q. For any angle $x^{\circ },x^c=$

1. $\frac{x°}{{\pi }^c}\times 180°$
2. $\frac{x°}{180°}\times {\pi }^c$
3. $x°\times {\pi }^c$

Q. Find the degree measure of ${\frac{\pi }{8}}^c$

Q. 1800" in sexagesimal system is equal to ​​​​​degrees in decimal degree system.

Q. Find the value of $\sin \left({270}^o\right)$.

Q. $\frac{\cos (90-A)\sin (90-A)}{\tan (90-A)}$=

1. ${\sin }^{2}A$
2. ${\cos }^{2}A$
3. $\sin A$
4. $1$

Q. If $b=14,c=11$, and $A={60}^o$, find B and C, given that
$log2=.30103$, $log3=.4771213$,
$L\tan {11}^o{44}^{\prime }=9.3174299$,
and $L\tan {11}^o{45}^{\prime }=9.3180640$.

Q. The measures of the interior angles taken in order of a polygon form an arithmetic sequence. The least measurement in the sequence is ${85}^{\circ }$. The greatest measurement is ${215}^{\circ }$. Find the number of sides in the given polygon

Q. ${35.47}^{\circ }$ is equivalent to

1. ${35}^{\circ }{28}^{\prime }{12}^{\prime \prime }$
2. ${35}^{\circ }{24}^{\prime }{12}^{\prime \prime }$
3. ${35}^{\circ }{28}^{\prime }{16}^{\prime \prime }$
4. ${35}^{\circ }{28}^{\prime }{18}^{\prime \prime }$

Q. Define a degree measure.

Q. $85.12°\mathrm{in}\mathrm{degree}\mathrm{decimal}\mathrm{system}\mathrm{can}\mathrm{be}\mathrm{expressed}\mathrm{in}\mathrm{sexagesimal}\mathrm{system}\mathrm{as}:$

1. $85°7\text{'}15\text{'}\text{'}$
2. $85°7\text{'}12\text{'}\text{'}$
3. $85°8\text{'}15\text{'}\text{'}$
4. $85°8\text{'}12\text{'}\text{'}$

Q. Express the following angles in degree, minutes and seconds.
$\frac{\pi }{8}$ radians

Q. Find $A:B:C$ if $4A=5B=6C$.

Q. The number of degrees in one acute angle of a right-angled triangle is equal to the number of grades in the other; express both the angles in degrees.

Q. Find the degree measure of ${\frac{2\pi }{15}}^c$

Q. 1800" in sexagesimal system is equal to ​​​​​degrees in decimal degree system.