Chapter 9.10, Problem 3PSA

a

To determine

To find:The value of $m\angle A$ when $\tan \angle A=1$ .

Answer to Problem 3PSA

The value of $m\angle A={45}^0$

Explanation of Solution

Given information:The following value has been given

  $\tan \angle A=1$

We find the value of $m\angle A$ as

  $m\angle A={\tan }^{-1}(1)$

And, we find from the trigonometric tables, that

  ${\tan }^{-1}(1)={45}^0$

Hence, we can say that

  $m\angle A={45}^0$

b

To determine

To find:The value of $m\angle A$ when $\sin \angle A=0.5$ .

Answer to Problem 3PSA

The value of $m\angle A={30}^0$

Explanation of Solution

Given information:The following value has been given

  $\sin \angle A=0.5$

We find the value of $m\angle A$ as

  $m\angle A={\sin }^{-1}(0.5)$

And, we find from the trigonometric tables, that

  ${\sin }^{-1}(0.5)={30}^0$

Hence, we can say that

  $m\angle A={30}^0$

c

To determine

To find:The value of $m\angle A$ when $\sin \angle A=\frac{\sqrt{3}}{2}$ .

Answer to Problem 3PSA

The value of $m\angle A={60}^0$

Explanation of Solution

Given information:The following value has been given

  $\sin \angle A=\frac{\sqrt{3}}{2}$

We find the value of $m\angle P$ as

  $m\angle A={\sin }^{-1}(\frac{\sqrt{3}}{2})$

And, we find from the trigonometric tables, that

  ${\sin }^{-1}(\frac{\sqrt{3}}{2})={60}^0$

Hence, we can say that

  $m\angle A={60}^0$