Chapter 8, Problem 13CT

(a)

To determine

To find: The measurement of the acute angle formed when the clock is at $10:00$ .

Answer to Problem 13CT

Acute angle form is ${60}^0$ .

Explanation of Solution

Given:

  

Concept used:

Obtuse triangles are those triangles which has one angle obtuse greater than ${90}^0$ .

Acute triangle has all angle less than ${90}^0$ .

The angle measure between any two consecutive numbers on a clock is $\frac{360}{12}=30$ .

Difference in second will be $\frac{30}{5}=6^0$ .

Calculation:

Since, the clock is a circle, it can say that it’s measure is ${320}^0$ and since there are $60\text{ min}$ it can find the degree of each turn of the minute hand by dividing $360$ with $60$ .

Therefore, it can say that each stripe on the clock is making the hands turn at $6^0$ .

The hour hand is at $10$ and the minute hand is at $12$ ,this has $10$ stripes. Therefore, the measure of the acute angle formed is $10\times 6={60}^0$ .

Hence, acute angle form is ${60}^0$ .

(b)

To determine

To find: the measurement of the obtuse angle formed when the clock is at $5:00$ .

Answer to Problem 13CT

Obtuse angle form is ${150}^0$ .

Explanation of Solution

Given:

  

Concept used:

Obtuse triangles are those triangles which has one angle obtuse greater than ${90}^0$ .

Acute triangle has all angle less than ${90}^0$ .

The angle measure between any two consecutive numbers on a clock is $\frac{360}{12}=30$ .

Difference in second will be $\frac{30}{5}=6^0$ .

Calculation:

Since, the clock is a circle, it can say that it’s measure is ${320}^0$ and since there are $60\text{ min}$ it can find the degree of each turn of the minute hand by dividing $360$ with $60$ .

Therefore, it can say that each stripe on the clock is making the hands turn at $6^0$ .

Since, an hour hand is at $5$ and the minute hand is at $12$ , this has $25$ stripes . therefore, the measure of the obtuse angle formed is $25\times 6={150}^0$ .

Hence, obtuse angle form is ${150}^0$ .

(c)

To determine

To find: the time where the hour and minute created a straight angle.

Answer to Problem 13CT

The time is $6:00$ .

Explanation of Solution

Given:

  

Concept used:

Obtuse triangles are those triangles which has one angle obtuse greater than ${90}^0$ .

Acute triangle has all angle less than ${90}^0$ .

The angle measure between any two consecutive numbers on a clock is $\frac{360}{12}=30$ .

Difference in second will be $\frac{30}{5}=6^0$ .

Calculation:

Since, the clock is a circle, it can say that it’s measure is ${320}^0$ and since there are $60\text{ min}$ it can find the degree of each turn of the minute hand by dividing $360$ with $60$ .

Therefore, it can say that each stripe on the clock is making the hands turn at $6^0$ .

Since, a straight angle has ${180}^0$ dividing this by $6^0$ will result to $30$ stripes.

To achieve $30$ stripes on the clock, it can put the hour hand at $6$ and minute hand at $12$ .

Hence, the time is $6:00$ .