Chapter 2.1, Problem 15PSC

a)

To determine

To Calculate: P ( $\angle ABC$ is acute )

Answer to Problem 15PSC

0.9

Explanation of Solution

Given information: $\text{m}\angle ABC={100}^{\circ }$

Formula: $\text{Probability}=\frac{\text{number of Favourable outcomes}}{\text{total numbers of possible outcomes}}$

  

  $\angle DBD$ Is acute if its measure is less than ${90}^{\circ }$

  $\therefore Probability=\frac{90}{100}=0.9$

b)

To determine

To Calculate: P ( $\angle DBC$ is acute )

Answer to Problem 15PSC

0.9

Explanation of Solution

Given information: $\text{m}\angle ABC={100}^{\circ }$

Formula: $\text{Probability}=\frac{\text{number of Favourable outcomes}}{\text{total numbers of possible outcomes}}$

  

  ${10}^{\circ }$ is acute if it’s measure is less than ${90}^{\circ }$

  $\therefore Probability=\frac{90}{100}=0.9$

c)

To determine

To Calculate: P (both $\angle ABC$ and $\angle DBC$ are acute)

Answer to Problem 15PSC

3) 0.8

Explanation of Solution

Given information: $\text{m}\angle ABC={100}^{\circ }$

Formula: $\text{Probability}=\frac{\text{number of Favourable outcomes}}{\text{total numbers of possible outcomes}}$

  

Both angles are acute if no angle range from $0^{\circ }$ to ${10}^{\circ }$

  $\therefore Probability=\frac{80}{100}=0.8$