Chapter 9.9, Problem 1PSA

a.

To determine

To find:A ratio formed by sine of angle A.

Answer to Problem 1PSA

The ratio formed by sine of angle A is $\frac{8}{17}$ .

Explanation of Solution

Given information:

A triangle with sides,

  $\begin{array}{l}AC=15,\\ AB=17,\\ BC=8.\end{array}$

Formula used:

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

Calculation:

  

In $\Delta ABC$ ,

  $sinA=\frac{oppositeside}{hypotenuseside}=\frac{8}{17}$

b.

To determine

To calculate: A ratio formed by cosine of angle A.

Answer to Problem 1PSA

The ratio formed by cosine of angle Ais $\frac{15}{17}$ .

Explanation of Solution

Given information:

A triangle with sides,

  $\begin{array}{l}AC=15,\\ AB=17,\\ BC=8.\end{array}$

Formula used:

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

Calculation:

  

In $\Delta ABC$ ,

  $\cos A=\frac{adjacentside}{hypotenuseside}=\frac{15}{17}$

c.

To determine

To find: A ratio formed by tangent of angle A.

Answer to Problem 1PSA

The ratio formed by tangent of angle A is $\frac{8}{15}$ .

Explanation of Solution

Given information:

A triangle with sides,

  $\begin{array}{l}AC=15,\\ AB=17,\\ BC=8.\end{array}$

Formula used:

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

Calculation:

  

In $\Delta ABC$ ,

  $\tan A=\frac{oppositeside}{adjacentside}=\frac{8}{15}$

d.

To determine

To find: A ratio formed by sine of angle B.

Answer to Problem 1PSA

The ratio formed by sine of angle B is $\frac{15}{17}$ .

Explanation of Solution

Given information:

A triangle with sides,

  $\begin{array}{l}AC=15,\\ AB=17,\\ BC=8.\end{array}$

Formula used:

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

Calculation:

  

In $\Delta ABC$ ,

  $\sin B=\frac{oppositeside}{hypotenuseside}=\frac{15}{17}$

e.

To determine

To calculate: A ratio formed by cosine of angle B.

Answer to Problem 1PSA

The ratio formed by cosine of angle B is $\frac{8}{17}$ .

Explanation of Solution

Given information:

A triangle with sides,

  $\begin{array}{l}AC=15,\\ AB=17,\\ BC=8.\end{array}$

Formula used:

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

Calculation:

  

In $\Delta ABC$ ,

  $\cos B=\frac{adjacentside}{hypotenuseside}=\frac{8}{17}$

f.

To determine

To find: A ratio formed by tangent of angle B.

Answer to Problem 1PSA

The ratio formed by tangent of angle B is $\frac{15}{8}$ .

Explanation of Solution

Given information:

A triangle with sides,

  $\begin{array}{l}AC=15,\\ AB=17,\\ BC=8.\end{array}$

Formula used:

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

Calculation:

  

In $\Delta ABC$ ,

  $\tan B=\frac{oppositeside}{adjacentside}=\frac{15}{8}$