Chapter 6, Problem 4PS

(a)

To determine

To draw: a diagram that gives a visual representation of the problem.

Explanation of Solution

Given information:

One side of the triangular courtyard is 52 feet long and another side is 46 feet long. The angle opposite the 52 foot side is $65°$ .

Calculation:

A visual representation of the problem is given below.

(b)

To determine

To find: the length of the third side of the courtyard.

Answer to Problem 4PS

The third side of the courtyard is 50.52 feet.

Explanation of Solution

Calculation:

Using the law of sines

  $\begin{array}{c}\frac{46}{\sin B}=\frac{52}{\sin 65°}\\ \sin B=\frac{46\sin 65°}{52}\\ =0.8017\\ B=53.296°\\ A=180-\left(53.296°+65°\right)=61.7°\end{array}$

Using the law of Sines again,

  $\begin{array}{c}\frac{52}{\sin 65°}=\frac{a}{\sin 61.7°}\\ a=\frac{52\sin 61.7°}{\sin 65°}\\ =50.52\end{array}$

The third side of the courtyard is 50.52 feet.

(c)

To determine

To find: the number of bags of grass to need cover the courtyard.

Answer to Problem 4PS

The number of bags of grass needed is 21.

Explanation of Solution

Given information:

One bag of grass seed covers an area of 50 square feet.

Calculation:

Area of the triangle is $\frac{1}{2}\times 46\times 52\times \sin 61.7°=1053.05{\text{ft}}^{\text{2}}$

The number of bags of grass needed is $\frac{1053.05}{50}\approx 21$ .