A gardener wants to flower a lawn which looks like a triangle. Find the area of lawn with given sides 8 and 4 while the angle between given sides is equal to 60?
area = 1/2 bc sinA
To find the area of a triangle with given side lengths and an included angle, you can use the formula:
Area = (1/2) * a * b * sin(C)
Where:
a and b are the lengths of the given sides of the triangle
C is the angle between the given sides
In this case, the given side lengths are 8 and 4, and the angle between them is 60 degrees.
So, plugging the values into the formula, we have:
Area = (1/2) * 8 * 4 * sin(60)
Now, let's calculate the value step-by-step.
Step 1: Convert the given angle from degrees to radians.
sin(60 degrees) = sin(pi/3 radians) = √3/2 (approximately 0.866)
Step 2: Plug the values into the formula:
Area = (1/2) * 8 * 4 * 0.866
Step 3: Simplify the expression:
Area = 16 * 0.866
Step 4: Calculate the final result:
Area ≈ 13.856 square units.
Therefore, the approximate area of the lawn, given the sides 8 and 4 with an angle of 60 degrees between them, is 13.856 square units.