if a=57 m, b=65 m, and ∠C=86 degrees, then what is the aea of △ ABC to the nearest meter
To find the area of a triangle, we can use the formula:
Area = (1/2) * base * height
In this case, we are given the lengths of sides a and b, but we need to find the height. We can use the sine formula to find the height:
sin(C) = opposite / hypotenuse
Since side a is opposite to angle C:
sin(C) = a / b
a = b * sin(C)
Substituting the given values:
a = 65m * sin(86 degrees) ≈ 64.07m
Now, we can calculate the area using the formula:
Area = (1/2) * a * b
Area = (1/2) * 64.07m * 65m
Area ≈ 2087.3m^2
Therefore, the area of triangle ABC is approximately 2087 square meters.