Two sides of a triangular field are 120m
and 200m.If the angle between the sides is 68 degrees. find the
area of the field in hectares
1/2(120)(200)sin68
=11126.206m squared
Area of a triangle = (1/2)(ab)sinØ
where a and b are sides with Ø as the angle between them.
Your data is perfectly suited for that formula
To find the area of the field, we can use the formula for the area of a triangle:
Area = (1/2) * base * height
In this case, the two given sides of the triangle act as the base and the height. However, we need to find the height of the triangle first.
We can use the sine formula to find the height:
height = side * sin(angle)
Given that one side is 120m and the angle between the sides is 68 degrees, we can calculate the height:
height = 120m * sin(68°)
Using a calculator, we can find that sin(68°) is approximately 0.92718. Therefore:
height = 120m * 0.92718
height = 111.2616m
Now that we have the base and the height of the triangle, we can calculate the area:
Area = (1/2) * 120m * 111.2616m
Area = 6661.896m²
Finally, to convert the area from square meters to hectares, we divide by 10,000 (since 1 hectare is equal to 10,000 square meters):
Area in hectares = 6661.896m² / 10,000
Area in hectares ≈ 0.6662 hectares
Therefore, the area of the field is approximately 0.6662 hectares.
To find the area of the field, we can use the formula for the area of a triangle:
Area = (1/2) * base * height
In this case, the two sides of the triangle form an angle of 68 degrees. We can use the formula for the area of a triangle given two sides and the included angle:
Area = (1/2) * a * b * sin(C)
Where a and b are the lengths of the two sides and C is the included angle.
Given that the two sides of the triangular field are 120m and 200m, and the included angle is 68 degrees, we can substitute these values into the formula to find the area.
Let's calculate the area using the given values:
Area = (1/2) * 120m * 200m * sin(68 degrees)
First, convert the angle from degrees to radians:
68 degrees = (68 * π) / 180 ≈ 1.19 radians
Now we can substitute the values into the formula and calculate the area:
Area = (1/2) * 120m * 200m * sin(1.19)
Area ≈ 1/2 * 120m * 200m * 0.9283 ≈ 13,983.24 square meters
To convert the area from square meters to hectares, we can use the conversion factor:
1 hectare = 10,000 square meters
So, to convert the area to hectares, divide the area in square meters by 10,000:
Area in hectares = 13,983.24 square meters / 10,000 ≈ 1.3983 hectares
Therefore, the area of the field is approximately 1.3983 hectares.