Chapter 9.9, Problem 16PSB

a

To determine

The statements have to be indicated as A, S or N.

Answer to Problem 16PSB

This statement is A

Explanation of Solution

Given information:The following equation has been given for triangle ABC with $\angle C={90}^0$

  $\sin \angle A=\cos \angle B$

We know that this statement is a theorem. Hence, it will always be true.

Thus, the statement is always true

b

To determine

The statements have to be indicated as Always (A), Sometimes(S) or Never(N) be true.

Answer to Problem 16PSB

This statement is N

Explanation of Solution

Given information:The following equation has been given for triangle ABC with $\angle C={90}^0$

  $\sin \angle A=\tan \angle A$

We know that the above statement can not be true for any given values of angles in a right triangle.

Thus, this statement is never true

c

To determine

To find: The given statement lies in which section i.e. A, S or N.

Answer to Problem 16PSB

This statement is S

Explanation of Solution

Given information:The following equation has been given for triangle ABC with $\angle C={90}^0$

  $\sin \angle A=\cos \angle A$

We know that for isosceles right triangles, when angles A and B are equal, this equation ca hold to be true.

Hence, this equation can be true sometimes.