Chapter 8.3, Problem 7CE

a.

To determine

To calculate: $x$.

Answer to Problem 7CE

  $10$ .

Explanation of Solution

Given information: $\angle 1$ is a right angle.

  

Calculation:

For,

  $\angle \text{ 1}$ to be a right angle, from the Pythagoras, $x=\sqrt{8^2+6^2}=10$ .

b.

To determine

To calculate: $x$.

Answer to Problem 7CE

  $x<10$ .

Explanation of Solution

Given information: $\angle \text{ 1}$ is an acute angle.

  

Calculation:

If, $\angle \text{ 1}$ is to be a right angle, from the Pythagoras, $x=\sqrt{8^2+6^2}=10$ .

Therefore, for acute angle $x$ must be less than $10$ , that is $x<10$ .

c.

To determine

To calculate: $x$.

Answer to Problem 7CE

  $x>10$ .

Explanation of Solution

Given information: $\angle \text{ 1}$ is an obtuse angle.

  

Calculation:

If, $\angle \text{ 1}$ is to be a right angle, from the Pythagoras, $x=\sqrt{8^2+6^2}=10$ .

Therefore, for obtuse angle $x$ must be greater than $10$ , that is $x>10$ .

d.

To determine

To calculate: $x$.

Answer to Problem 7CE

  $x=6$ or $x=8$ .

Explanation of Solution

Given information: Triangle is isosceles.

  

Calculation:

For an isosceles triangle, two sides of a triangle should be equal

Therefore, $x$ must 6 or 8.

e.

To determine

To calculate: $x$.

Answer to Problem 7CE

  $x>14$ .

Explanation of Solution

Given information: No triangle is possible.

  

Calculation:

If the sum of length of two sides of a triangle is less than the third side, the triangle will not be possible.

Therefore, for “ no triangle possible” case, third side should be greater than the sum of other two sides,

  $\Rightarrow x>(6+8)$ ,

  $\Rightarrow x>14$ .