if a=57 m, b=65 m, and ∠C=86 degrees, then what is the aea of △ ABC to the nearst meter
To find the area of triangle ABC, you can use the formula for the area of a triangle:
Area = 1/2 * base * height
In this case, you know the lengths of sides a and b, but you need to find the height.
To find the height, you can use the sine function, since you know one angle and the length of the side opposite that angle.
sin(C) = height / side b
Rearranging the equation, you get:
height = sin(C) * side b
Using the values given, you can calculate the height:
height = sin(86 degrees) * 65 m
= 0.9962 * 65 m
≈ 64.7713 m
Now that you have the base and the height, you can calculate the area:
Area = 1/2 * base * height
= 1/2 * 57 m * 64.7713 m
≈ 1840.6965 m²
Rounding to the nearest meter, the area of triangle ABC is approximately 1841 m².