if a=57 m, b=65 m, and ∠C=86 degrees, then what is the aea of △ ABC to the nearest meter if m^2
To calculate the area of a triangle, we can use the formula: area = (1/2) * base * height.
In the given triangle ABC, we have the following information:
- Side a = 57 m
- Side b = 65 m
- Angle C = 86 degrees
To find the height of the triangle, we can use the sine function. Since the sine of an angle is equal to the opposite side divided by the hypotenuse, we have sin(C) = a / b. Rearranging the formula, we get a = sin(C) * b.
Therefore, a = sin(86°) * 65 m ≈ 63.452 m.
Now, we can calculate the area using the formula:
area = (1/2) * a * c
= (1/2) * 57 m * 63.452 m ≈ 1806.978 m^2.
Rounding to the nearest meter, the area of △ABC is approximately 1807 m^2.