Tag: angle and their measurement

Quizzes (6) Questions (67)

Questions Related to angle and their measurement

Multiple choice mathematics and statistics angle and their measurement degree measure of angle measure of angle radians or degrees

The value of $\tan\left(7\dfrac{1}{2}\right)^o$ is 

  1. $\dfrac {2\sqrt 2 -(1+\sqrt 3)}{\sqrt 3-1}$
  2. $\dfrac {1+\sqrt 3}{1-\sqrt 3}$
  3. $\dfrac {1}{\sqrt 3}+\sqrt 3$
  4. $\sqrt 2 +\sqrt 3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\tan\left(7\dfrac{1}{2}\right)^o=\tan\left(\dfrac{15}{2}\right)^o$


                       $=\dfrac{\sin\dfrac{15^o}{2}}{\cos\dfrac{15^o}{2}}$

                       $=\dfrac{2\sin\dfrac{15^o}{2}\times \sin\dfrac{15^o}{2}}{2\sin\dfrac{15^o}{2}\times \cos\dfrac{15^o}{2}}$

                        $=\dfrac{2\sin^2\dfrac{15^o}{2}}{\sin\left(2\times\dfrac{15^o}{2}\right)}$

                        $=\dfrac{1-\cos\left(2\times\dfrac{15^o}{2}\right)}{\sin 15^o}$

                        $=\dfrac{1-\cos 15^o}{\sin 15^o}$

Now,
$\cos 15^o=\cos(45^o-30^o)$
              $=\cos 45^o\cos30^o+\sin 45^o\sin 30^o$
              $=\dfrac{1}{\sqrt{2}}\times\dfrac{\sqrt{3}}{2}+\dfrac{1}{\sqrt{2}}\times\dfrac {1}{2}$
              $=\dfrac{\sqrt{3}+1}{2\sqrt{2}}$

$\sin 15^o=\sin(45^o-30^o)$
             $=\sin 45^o\cos30^o-\cos 45^o\sin 30^o$
             $=\dfrac{1}{\sqrt{2}}\times\dfrac{\sqrt{3}}{2}-\dfrac{1}{\sqrt{2}}\times\dfrac {1}{2}$
             $=\dfrac{\sqrt{3}-1}{2\sqrt{2}}$


$\tan\left(7\dfrac{1}{2}\right)^o=\dfrac{1-\dfrac{\sqrt{3}+1}{2\sqrt{2}}}{\dfrac{\sqrt{3}-1}{2\sqrt{2}}}$

                      $=\dfrac{2\sqrt{2}-(\sqrt{3}+1)}{\sqrt{3}-1}$

Multiple choice mathematics and statistics angle and their measurement angles and sides naming the sides in a right angled triangle understanding ratios

Value of $ \displaystyle \sin 45^{\circ} \cos 45 \left ( \tan 45^{\circ}+\cot 45^{\circ} \right )^{2}   $  is 

  1. $1$
  2. $2$
  3. $3$
  4. $4$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$ \displaystyle \sin 45^{\circ} \cos 45 \left ( \tan 45^{\circ}+\cot 45^{\circ} \right )^{2}   $

$=\dfrac{1}{\sqrt2} \times \dfrac{1}{\sqrt2} (1+1)^2 $


$=\dfrac42$

$=2$

Multiple choice mathematics and statistics angle and their measurement angles and sides naming the sides in a right angled triangle understanding ratios

Two angles are called adjacent if

  1. they lie in the same plane and have a common vertex

  2. they have a ray in common

  3. the intersection of their interiors is empty

  4. all the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Two angles are called adjacent if
they lie in same plane and have a common vertex,they have a ray in common and the intersection of their interiors is empty.
do (D) all the above is correct

Multiple choice mathematics and statistics angle and their measurement angles and sides naming the sides in a right angled triangle understanding ratios

In a cyclic quadrilateral ABCD, $\displaystyle \angle ABC=60^{\circ}$ and if O be the centre of the circle then the measure of $\displaystyle \angle OAC$ is

  1. $\displaystyle 20^{\circ}$
  2. $\displaystyle 30^{\circ}$
  3. $\displaystyle 40^{\circ}$
  4. $\displaystyle 50^{\circ}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In a cyclic quadrilateral, the angle subtended by a chord at the center is twice the angle at the circumference. If angle ABC = 60, the central angle AOC = 120. In triangle OAC, OA = OC (radii), so angle OAC = (180 - 120)/2 = 30 degrees.

Multiple choice mathematics and statistics angle and their measurement angles and sides naming the sides in a right angled triangle understanding ratios

In the early 9th century AD, _________ produced accurate sine and cosine tables, and the first table of tangents.

  1. Habash al-Hasib al-Marwazi

  2. Muhammad ibn Jabir al-Harrani al-Battani

  3. Muhammad ibn Musa al-Khwarizmi

  4. Abu al-Wafa al-Buzjani
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In the early 9th century AD, Muhammad ibn Mūsā al-Khwārizmī produced accurate sine and cosine tables, and the first table of tangents. He was also a pioneer in spherical trigonometry.

Multiple choice mathematics and statistics angle and their measurement angles and sides naming the sides in a right angled triangle understanding ratios

The first recorded use of trigonometry came from the Hellenistic mathematician ________________.

  1. William Rowan Hamilton

  2. Hipparchus

  3. Newton

  4. Bartholomaeus Pitiscus
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The first recorded use of trigonometry came from the Hellenistic mathematician Hipparchus.

So, option B is correct.