Question

Frank is building a triangular garden. He wants to know how much sod he will need to buy for the area. The measurements for the garden are; bade 30 ft one side 32 ft second side 31ft and the height if we were standing up would it be 33 ft how much sod does frank need to buy

Answer 1

The amount of soil required must be enough to cover an area of A = 415.27 ft^2

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 )

Where, θ : It is the included angle opposite to side "c".

- To determine the angle ( θ ) using cosine rule:

cos ( θ ) =

`(a^2 + b^2 - c^2)/(2*a*b)\\\\(30^2 + 32^2 - 31^2)/(2*30*32)\\\\`

cos ( θ ) = 0.501562

θ = 59.9°

- Compute the area A:

A = 0.5*30*32*sin ( 59.9 )

A = 415.27 ft^2

- The amount of soil required must be enough to cover an area of A = 415.27 ft^2

Answer 2

He needs to buy at least 495 square feet of sod.

Explanation:

Please kindly check the attached file for explanation.