A farmer is estimating the surface area of his barn to find how much paint he needs to buy. One part of the barn is triangular as shown.

The base of the triangle is 22 meters long
Both angles on either side connecting the base to each leg is 30 degrees. (It looks like an isosceles triangle)

a. The darkened sides in the figure are the edges of the roof. This trim will be painted white. Find the length of each of these two sides of the triangle. Explain how you found the answer.

b. The triangular surface will be painted red. Find the area of the triangle. Explain how you found the answer.

I know it has something to do with using cosine... but I'm not sure how to do it. Step by step would be the best!:) Please? Thank you!

  1. 👍
  2. 👎
  3. 👁
  1. By the sine law, we know that

    sin(<A)/A is sin(<B)/B which is equal to sin(<C)/C.

    sin(<120)/22m = sin(<30)/x

    We need to isolate x.

    x= 22m * (sin 30 degrees/sin 120 degrees)

    Since we have an isosceles triangle, each side is about 12.7m.

    PART B

    We need to find the area of the triangle.

    The formula for area is base x height /2 .

    Our height we need to find out with the pythagorean theorem. half of our triangle means a length of the triangle at 11m.


    Therefore, (12.7)^2=11^2+x^2

    Our height is 6.35084703891 m.

    Base x height /2= area
    area= 6.35084703891 m * 11 m / 2= 34.929658714m.

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    A farmer decides to enclose a rectangular garden, using the side of a barn as one side of the rectangle. What is the maximum area that the farmer can enclose with 80ft of fence? 800 sq ft? What should the dimensions of the garden

  2. Calculus

    A farmer has 1500 feet of fencing in his barn. He wishes to enclose a rectangular pen. Subdivided into two regions by a section of fence down the middle, parallel to one side of the rectangle. Express the area enclosed by the pen

  3. Math

    A farmer has 80 feet of fencing, which she plans to use to fence in a plot of land for a pigpen. If she chooses to enclose a plot along the broad side of her barn, what is the largest area that can be enclosed? (Note: The side

  4. math

    A farmer wants to fence a small rectangular yard next to a barn. Fence for side parallel to the barn will cost 75 per foot and the fence for the other two sides will cost 30 per foot. The farmer has a total of 1750 dollars to

  1. math

    a farmer wants to build a rectangular pen using a side of a barn and 60ft of fence. find the dimensions and area of the largest such pen

  2. calc

    A farmer intends to fence o a rectangular pen for his pig Wilbur, using the barn as one of the sides. If the enclosed area is to be 50 square feet, what is smallest amount of fence needed, in feet?

  3. math

    A farmer has 90 meters of fencing and would like to use the fencing to create a rectangular garden where one of the sides of the garden is against the side of a barn. Let L represent the varying length of the rectangular garden

  4. calculus optimization problem

    A farmer has 460 feet of fencing with which to enclose a rectangular grazing pen next to a barn. The farmer will use the barn as one side of the pen, and will use the fencing for the other three sides. find the dimension of the

  1. Math

    The amount of paint p needed to paint the walls of a room varies directly as the area A of the wall. If two gallons of paint is needed to paint a 40 sq meter wall, how many gallons of paint are needed to paint a wall with an area

  2. algebra

    A farmer decides to enclose a rectangular garden, using the side of a barn as one side of the rectangle. What is the maximum area that the farmer can enclose with 100 ft. of fence? What should the dimensions of the garden be to

  3. math

    samuel is painting the toy chest shown in the diagram (including the bottom). He needs to know the surface area to determine how much paint to buy.Which of the following is the surface area of the chest.

  4. physics

    A charged paint is spread in a very thin uniform layer over the surface of a plastic sphere of diameter 19.0{\rm cm} , giving it a charge of -13.0\mu {\rm C} Find the electric field just outside the paint layer. Find the electric

You can view more similar questions or ask a new question.