Chapter 9.9, Problem 4PSA

a.

To determine

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

Answer to Problem 4PSA

The ratio formed by cosine of angle H is $\frac{39}{89}$ .

Explanation of Solution

Given information:

A right angle triangleHJK with sides,

  $\begin{array}{l}KH=8.9,\\ HJ=3.9,\\ KJ=8.\end{array}$

Formula used:

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

Calculation:

  

In $\Delta HJK$ ,

  $cos\angle H=\frac{adjacentside}{hypotenuseside}=\frac{HJ}{HK}=\frac{3.9}{8.9}=\frac{39}{89}$

b.

To determine

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

Answer to Problem 4PSA

The ratio formed by tangent of angle Kis $\frac{39}{80}$ .

Explanation of Solution

Given information:

A right angle triangle HJK with sides,

  $\begin{array}{l}KH=8.9,\\ HJ=3.9,\\ KJ=8.\end{array}$

Formula used:

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

Calculation:

  

In $\Delta HJK$ ,

  $\tan \angle K=\frac{adjacentside}{hypotenuseside}=\frac{HJ}{KJ}=\frac{3.9}{8}=\frac{39}{80}$