Chapter 13, Problem 7CUR

a.

To determine

To calculate: the value of $\cos A$ .

Answer to Problem 7CUR

The value of $\cos A$ is $\frac{1}{3}$ .

Explanation of Solution

Given information: In $\Delta ABC,AB\perp BC,AB=1,\&AC=3$ .

Calculation:

  $\begin{array}{l}B{C}^2=3^2-1^2\\ B{C}^2=9-1\\ B{C}^2=8\\ BC=2\sqrt{2}\\ \cos A=\frac{AB}{AC}=\frac{1}{3}\end{array}$

b.

To determine

To calculate: the value of $\sin C$ .

Answer to Problem 7CUR

The value of $\sin C$ is $\frac{1}{3}$ .

Explanation of Solution

Given information: In $\Delta ABC,AB\perp BC,AB=1,\&AC=3$ .

Calculation:

  $\sin C=\frac{AB}{AC}=\frac{1}{3}$

c.

To determine

To calculate: the value of $\tan A$ .

Answer to Problem 7CUR

The value of $\tan A$ is $2\sqrt{2}$ .

Explanation of Solution

Given information: In $\Delta ABC,AB\perp BC,AB=1,\&AC=3$ .

Calculation:

  $\begin{array}{l}B{C}^2=3^2-1^2\\ B{C}^2=9-1\\ B{C}^2=8\\ BC=2\sqrt{2}\\ \tan A=\frac{BC}{AB}=\frac{2\sqrt{2}}{1}=2\sqrt{2}\end{array}$

d.

To determine

To calculate: the value of $\cos C$ .

Answer to Problem 7CUR

The value of $\cos C$ is $\frac{2\sqrt{2}}{3}$ .

Explanation of Solution

Given information: In $\Delta ABC,AB\perp BC,AB=1,\&AC=3$ .

Calculation:

  $\begin{array}{l}B{C}^2=3^2-1^2\\ B{C}^2=9-1\\ B{C}^2=8\\ BC=2\sqrt{2}\\ \cos C=\frac{BC}{AC}=\frac{2\sqrt{2}}{3}\end{array}$