Question

Find the number of right angles turned through by the hour hand of a clock when its goes from;
$\left( 1 \right)3$ to $6$
$\left( 2 \right)2$ to $8$
$\left( 3 \right)5$ to $11$
$\left( 4 \right)10$ to $1$
$\left( 5 \right)12$ to $9$
$\left( 6 \right)12$ to $6$

Answer 1

Hint:To solve this question, we must be familiar with some basic concepts of clocks. The hour hand of a properly functioning clock revolves ${360^0}$ in one complete revolution. In other words, we can say that the hour hand forms $4$ right angle triangles in one revolution of a clock. Here, one revolution means a complete $12$ hour period.

Complete step by step answer:
Presented below is the basic representation of a clock;

$ \Rightarrow {\text{One revolution = 12 hours = }}{360^0}$
Therefore, ${\text{one hour = }}\dfrac{{{{360}^0}}}{{12}} = {\text{3}}{{\text{0}}^0}$
$\left( 1 \right)3{\text{ to 6}}$:
From $3{\text{ to 6}}$, the time difference is $6 - 3{\text{ = 3 hours}}$. By interpretation, we can say that the hour hand revolves by ${90^0}$ or $1$ right angled triangle.
Or by the formula, we can solve easily;
$ \Rightarrow 3 \times \dfrac{{{{360}^0}}}{{12}} = {90^0}$
Therefore, the correct answer for this question is ${90^o}$ i.e. one right angle triangle.

$\left( 2 \right){\text{2 to 8}}$:
From ${\text{2 to 8}}$, the time difference is $8 - 2{\text{ = 6 hours}}$. By interpretation, we can say that the hour hand revolves by ${180^0}$ or $2$ right angled triangles.
Or by the formula, we can solve easily;
$ \Rightarrow 6 \times \dfrac{{{{360}^0}}}{{12}} = {180^0}{\text{ or 9}}{{\text{0}}^0} + {90^0}$
Therefore, the correct answer for this question is ${180^0}$ i.e. two right angle triangles.

$\left( 3 \right){\text{5 to 11}}$:
From ${\text{5 to 11}}$, the time difference is ${\text{11 - 5 = 6 hours}}$. By interpretation, we can say that the hour hand revolves by ${180^0}$ or $2$ right angled triangles.
Or by the formula, we can solve easily;
$ \Rightarrow 6 \times \dfrac{{{{360}^0}}}{{12}} = {180^0}{\text{ or 9}}{{\text{0}}^0} + {90^0}$
Therefore, the correct answer for this question is ${180^0}$ i.e. two right angle triangles.

$\left( 4 \right){\text{10 to 1}}$:
From ${\text{10 to 1}}$, the time difference is ${\text{10 - 1 = 3 hours}}$. By interpretation, we can say that the hour hand revolves by ${90^0}$ or 1 right angled triangles.
Or by the formula, we can solve easily;
$ \Rightarrow 3 \times \dfrac{{{{360}^0}}}{{12}} = {90^0}{\text{ }}$
Therefore, the correct answer for this question is ${90^0}$ i.e. one right angle triangle.

$\left( 5 \right){\text{12 to 9}}$:
From ${\text{12 to 9}}$, the time difference is ${\text{12 - 9 = 9 hours}}$. By interpretation, we can say that the hour hand revolves by ${180^0}$ or $2$ right angled triangles.
Or by the formula, we can solve easily;
$ \Rightarrow 9 \times \dfrac{{{{360}^0}}}{{12}} = {270^0}{\text{ }}$or ${90^0} + {90^0} + {90^0}$
Therefore, the correct answer for this question is ${270^0}$ i.e. three right angle triangles.

$\left( 6 \right){\text{12 to 6}}$:
From ${\text{12 to 6}}$, the time difference is ${\text{12 - 6 = 6 hours}}$. By interpretation, we can say that the hour hand revolves by ${180^0}$ or $2$ right angled triangles.
Or by the formula, we can solve easily;
$ \Rightarrow 6 \times \dfrac{{{{360}^0}}}{{12}} = {180^0}{\text{ }}$or ${90^0} + {90^0}$
Therefore, the correct answer for this question is ${180^0}$ i.e. two right angle triangles.

Note:We should be familiar with the basic concepts of clocks in order to solve this question. A clock is a complete circle having ${360^0}$. It can be divided into $12$ equal parts , each part is $\dfrac{{{{360}^0}}}{{12}} = {30^0}$. The hour hand completes ${360^0}$ in 12 hours and ${30^0}$ in $1$ hour . The minute hand completes ${360^0}$ in $60$ minutes and ${6^0}$ in $1$ minute.