Answer:
He needs to buy at least 495 square feet of sod.
Step-by-step explanation:
Please kindly check the attached file for explanation.
Answer:
The amount of soil required must be enough to cover an area of A = 415.27 ft^2
Step-by-step explanation:
Given:-
- Frank is to buy soil for his rectangular garden with the following dimensions.
     Side ( a ) = 30 ft
     Side ( b ) = 32 ft
     Side ( c ) = 31 ft
     height ( h ) = 33 ft
Find:-
He wants to know how much soil he will need to buy for the area.
Solution:-
- The amount of soil required for his triangular shaped garden is determine by the area of the triangle with sides a , b, and c given.
- The area ( A ) of a triangle is:
       A = 0.5*a*b*sin ( θ )   Â
Where, θ : It is the included angle opposite to side "c".
- To determine the angle ( θ ) using cosine rule:
    cos ( θ ) =
             [tex]\frac{a^2 + b^2 - c^2}{2*a*b}\\\\\frac{30^2 + 32^2 - 31^2}{2*30*32}\\\\[/tex]
    cos ( θ ) =  0.501562
    θ = 59.9°
- Compute the area A:
       A = 0.5*30*32*sin ( 59.9 )
       A = 415.27 ft^2   Â
- The amount of soil required must be enough to cover an area of A = 415.27 ft^2
