if a=57 m, b=65 m, and ∠C=86 degrees, then what is the aea of △ ABC
To find the area of triangle ABC, we can use the formula:
Area = (1/2) * base * height
In this case, we don't know the height of the triangle. However, we can use the given information to find the height using trigonometry.
First, let's find the length of side c. We can use the Law of Cosines:
c^2 = a^2 + b^2 - 2ab * cos(C)
c^2 = 57^2 + 65^2 - 2 * 57 * 65 * cos(86)
c^2 = 3249 + 4225 - 2 * 57 * 65 * (-0.087)
c^2 = 3249 + 4225 + 3997.2
c^2 = 11471.2
c ≈ 107.12 m
Now, let's find the height using the sine of angle C:
sin(C) = height / c
height = c * sin(C)
height = 107.12 * sin(86)
height ≈ 105.53 m
Now that we know the height, we can find the area:
Area = (1/2) * base * height
Area = (1/2) * 57 * 105.53
Area ≈ 3023.33 square meters
Therefore, the area of triangle ABC is approximately 3023.33 square meters.