Chapter 11.2, Problem 34WE

(a)

To determine

Find the area of the parallelogram when $m\angle C=30°$

Answer to Problem 34WE

100

Explanation of Solution

Given:

  

Calculation:

The base of the parallelogram is b = 20.

The height of the parallelogram is h = $10\sin C=10\sin 30°=10\cdot \frac{1}{2}=5$

So, the area of the parallelogram = $A=bh=20\cdot 5=100$

(b)

To determine

Find the area of the parallelogram when $m\angle C=45°$

Answer to Problem 34WE

  $100\sqrt{2}$

Explanation of Solution

Given:

  

Calculation:

The base of the parallelogram is b = 20.

The height of the parallelogram is h = $10\sin C=10\sin 45°=10\cdot \frac{\sqrt{2}}{2}=5\sqrt{2}$

So, the area of the parallelogram = $A=bh=20\cdot 5\sqrt{2}=100\sqrt{2}$

(c)

To determine

Find the area of the parallelogram when $m\angle C=60°$

Answer to Problem 34WE

  $100\sqrt{3}$

Explanation of Solution

Given:

  

Calculation:

The base of the parallelogram is b = 20.

The height of the parallelogram is h = $10\sin C=10\sin 60°=10\cdot \frac{\sqrt{3}}{2}=5\sqrt{3}$

So, the area of the parallelogram = $A=bh=20\cdot 5\sqrt{3}=100\sqrt{3}$

(d)

To determine

Find the area of the parallelogram when $m\angle C=90°$

Answer to Problem 34WE

200

Explanation of Solution

Given:

  

Calculation:

The base of the parallelogram is b = 20.

The height of the parallelogram is h = $10\sin C=10\sin 90°=10\cdot 1=10$

So, the area of the parallelogram = $A=bh=20\cdot 10=200$

(e)

To determine

Find the area of the parallelogram when $m\angle C=120°$

Answer to Problem 34WE

  $100\sqrt{3}$

Explanation of Solution

Given:

  

Calculation:

The base of the parallelogram is b = 20.

The height of the parallelogram is h = $10\sin C=10\sin 120°=10\sin (90°+30°)=10\cos 30°=10\cdot \frac{\sqrt{3}}{2}=5\sqrt{3}$

So, the area of the parallelogram = $A=bh=20\cdot 5\sqrt{3}=100\sqrt{3}$

(f)

To determine

Approximate the answers in part (b), (c), and (e) using $\sqrt{2}\approx 1.4\text{ and }\sqrt{3}\approx 1.7$ .Then record answers from (a)-(e) on a set of axes.

Answer to Problem 34WE

  $100\sqrt{3}$

Explanation of Solution

Given:

  

Calculation:

From part (a), when $m\angle C=30°$ , $A=100$

From part (b) , when $m\angle C=45°$ , $A=100\sqrt{2}\approx 100\times 1.4=140$

From part (c), $m\angle C=60°$ , $A=100\sqrt{3}\approx 100\times 1.7=170$

From part (d), when $m\angle C=90°$ , $A=200$

From part (e), $m\angle C=120°$

  $A=100\sqrt{3}\approx 100\times 1.7=170$

Represent the information on axes: