Chapter 9.9, Problem 6PSA

a.

To determine

To find:The missing angle by using trigonometric ratios.

Answer to Problem 6PSA

Themissing angle is $\tan \angle A$ .

Explanation of Solution

Given information:

Side $CB=5,$

Side $AC=12,$

Side $AB=13.$

Formula used:

  $\tan \theta =\frac{oppositeside}{adjacentside}$

Calculation:

  

We know that $\tan \theta =\frac{oppositeside}{adjacentside}$

  $\tan \angle A=\frac{oppositeside}{adjacentside}=\frac{BC}{CA}=\frac{5}{12}$

b.

To determine

To calculate: The missing angle by matching the correct trigonometric formula.

Answer to Problem 6PSA

The missing angle is $\cos \angle A$ .

Explanation of Solution

Given information:

Side $CB=5,$

Side $AC=12,$

Side $AB=13.$

Formula used:

  $cos\theta =\frac{adjacentside}{hypotenuseside}$

Calculation:

  

We know that $cos\theta =\frac{adjacentside}{hypotenuseside}$

  $\cos \angle A=\frac{adjacentside}{hypotenuseside}=\frac{AC}{AB}=\frac{12}{13}$

c.

To determine

To find: The missing angle by comparing with correct trigonometric ratios.

Answer to Problem 6PSA

The angle is $\sin \angle A$ .

Explanation of Solution

Given information:

Side $CB=5,$

Side $AC=12,$

Side $AB=13.$

Formula used:

  $\sin \theta =\frac{oppositeside}{hypotenuseside}$

Calculation:

  

We know that $\sin \theta =\frac{oppositeside}{hypotenuseside}$

  $\sin \angle A=\frac{oppositeside}{hypotenuseside}=\frac{CB}{AB}=\frac{5}{13}$