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
We can find the base by using the length of side a and side b. Since angle C is given, we can use the Law of Cosines to find the length of side c:
c^2 = a^2 + b^2 - 2ab*cos(C)
c^2 = 57^2 + 65^2 - 2(57)(65)*cos(86)
c^2 = 3249 + 4225 - 7425*cos(86)
c^2 ≈ 130.02
Taking the square root of both sides:
c ≈ √130.02 ≈ 11.40
Now we can find the height of triangle ABC. We can drop a perpendicular from angle C to side AB. This perpendicular will be the height of the triangle.
Let h be the height.
Using Trigonometry (specifically Sin), we can find the height:
sin(C) = h/c
sin(86) = h/11.40
h ≈ sin(86) * 11.40 ≈ 11.33
Finally, we can calculate the area of triangle ABC:
Area = (1/2) * base * height
Area ≈ (1/2) * 57 * 11.33 ≈ 324.99
Therefore, the area of triangle ABC to the nearest meter is approximately 325 m^2.