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 find the area of triangle ABC, we can use the formula: Area = (1/2) * base * height.
In this case, we have two sides of the triangle, a and b, and the angle C. To find the height of the triangle, we need to use trigonometry.
First, we need to find side c using the Law of Cosines:
c^2 = a^2 + b^2 - 2*a*b*cos(C)
c^2 = (57)^2 + (65)^2 - 2*(57)*(65)*cos(86)
c^2 ≈ 3249 + 4225 - 2(3726.81)(0.08716)
c^2 ≈ 7474.69 - 647.23
c^2 ≈ 6827.46
c ≈ √6827.46
c ≈ 82.64 m
Now that we have side c, we can find the height (h) using the formula: h = b*sin(C)
h = 65 * sin(86)
h ≈ 65 * 0.99985
h ≈ 64.99 m
Now we can find the area:
Area = (1/2) * base * height
Area = (1/2) * a * h
Area = (1/2) * 57 * 64.99
Area ≈ 1845.075 m^2
Therefore, the area of triangle ABC to the nearest meter is approximately 1845 m^2.