Question

A homeowner has a yard that forms a triangle. He needs to buy seed and fertilizer for the yard. To do this, he needs to know the size of the yard. Two of the sides measure 53ft and 42ft and form an included angle of 135°. What it the size of the yard to the nearest square foot?

Answer 1

The size of the yard is approximately 67.6841ft to the nearest square foot. To find the size of the yard, we can use the Law of Cosines.

Step-by-step explanation:

To find the size of the yard, we can use the Law of Cosines. The Law of Cosines states that for any triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of the lengths of those two sides multiplied by the cosine of the included angle.

Let's label the sides of the triangle as follows:

• a = 53ft
• b = 42ft
• c = unknown (size of the yard)

And the included angle as:

• A = 135°

Using the Law of Cosines, we have:

c^2 = a^2 + b^2 - 2ab*cos(A)

c^2 = 53^2 + 42^2 - 2*53*42*cos(135°)

c^2 = 2809 + 1764 - 2*53*42*(-0.7071)

c^2 = 4573.3499

c ≈ √(4573.3499) ≈ 67.6841ft

Therefore, the size of the yard is approximately 67.6841ft to the nearest square foot.