wendell is setting concrete on a triangular patio. one side of the patio is 12.9 feet and another side is 15.2 feet. the angle opposite the 15.2 foot side is 68 degrees. one bag of concrete covers an area of 5 square feet. how many bags of concrete will wendell need to cover the patio?
using the law of sines,
the angle opposite the 12.9' side is 52°
the remaining angle is thus 60°
area is 1/2 * 15.2 * (12.9 sin 60°) = 85 ft^2
85/5 = 17 bags
Well, it seems like Wendell is really on a solid mission here! Okay, let's crunch some numbers. to find the area of the triangular patio, we can use the formula:
Area = (1/2) * Base * Height
Since we don't have the height, we'll have to find it using the Law of Sines. But before we get all mathematical, let me bring in some circus vibes. *cue circus music*
Alright, now back to the numbers. According to the Law of Sines:
sin(A)/a = sin(B)/b = sin(C)/c
In this case, we know angle A is 68 degrees, side a is 15.2 feet, and side b is 12.9 feet. So, we can rearrange this equation to find the height:
sin(68) / 15.2 = sin(C) / 12.9
Now let's do some calculations. *pulls out a tiny calculator and starts pressing buttons*
sin(C) = (sin(68) * 12.9) / 15.2
sin(C) ≈ 0.8604
Now, since we're dealing with a right triangle, the angle opposite the height is 90 degrees, so we can use sin(C) = height / hypotenuse.
0.8604 = height / 15.2
height ≈ 0.8604 * 15.2
height ≈ 13.10 feet
Aha! Now we have the height, which means we can find the area:
Area = (1/2) * Base * Height
Area ≈ (1/2) * 15.2 * 13.10
Area ≈ 99.86 square feet
Great! So, the triangular patio has an area of approximately 99.86 square feet.
Since one bag of concrete covers 5 square feet, we can divide the total area by 5 to find out how many bags Wendell will need:
Number of bags = Area / 5
Number of bags ≈ 99.86 / 5
Number of bags ≈ 19.97
Well, Wendell will need about 19.97 bags of concrete. But since we can't have a 0.97 of a bag, he might want to round up to be on the safe side. So let's say, 20 bags should do the trick!
Now, let's get this patio set in stone so Wendell can have a concrete success! 🎪🌿🌼
To find out how many bags of concrete Wendell will need to cover the patio, we need to calculate the total area of the triangular patio first.
Step 1: Calculate the area of the triangular patio.
To calculate the area of a triangle, we can use the formula:
Area = (1/2) * base * height
Step 2: Calculate the height of the triangle.
To calculate the height, we can use trigonometry. Since we know the angle opposite the given side, we can use the sine function.
height = sin(angle) * side
In this case, the side is 15.2 feet, and the angle is 68 degrees.
Step 3: Calculate the area of the triangle.
Multiply the base (12.9 feet) by the calculated height to get the area.
Step 4: Calculate the number of bags of concrete needed.
Divide the total area of the patio by the coverage area of one bag of concrete (5 square feet) to get the number of bags needed.
Let's calculate each step to find the answer:
Step 1:
Area = (1/2) * 12.9 feet * height
Step 2:
height = sin(68 degrees) * 15.2 feet
Using a calculator, sin(68 degrees) ≈ 0.9272
height = 0.9272 * 15.2 feet
Step 3:
Area = (1/2) * 12.9 feet * (0.9272 * 15.2 feet)
Step 4:
Number of bags = Area / Coverage area per bag
Number of bags = (12.9 feet * 0.9272 * 15.2 feet) / 5 square feet
Now, let's calculate the final step:
Number of bags = (12.9 * 0.9272 * 15.2) / 5
Number of bags ≈ 44.41
Therefore, Wendell will need approximately 44 bags of concrete to cover the triangular patio.
To find out how many bags of concrete Wendell will need to cover the patio, we first need to find the area of the triangular patio.
To find the area of a triangle, we can use the formula:
Area = (1/2) * base * height
In this case, the base of the triangle is 12.9 feet, and the height can be found by using the sine of the angle opposite the 15.2-foot side.
We can use the formula:
sin(angle) = opposite/hypotenuse
Rearranging the formula, we get:
height = hypotenuse * sin(angle)
In this case, the hypotenuse is 15.2 feet, and the angle opposite it is 68 degrees. So, we can calculate the height as follows:
height = 15.2 * sin(68)
Now we can calculate the area of the triangular patio:
Area = (1/2) * 12.9 * (15.2 * sin(68))
Finally, to find out how many bags of concrete we'll need, we divide the area of the triangular patio by the coverage area of one bag of concrete (5 square feet).
Number of bags = Area / 5
Let's calculate it step by step:
1. Calculate the height:
height = 15.2 * sin(68)
2. Calculate the area of the triangular patio:
Area = (1/2) * 12.9 * (15.2 * sin(68))
3. Calculate the number of bags of concrete:
Number of bags = Area / 5
Plug in the values and do the calculations to get the final answer.