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
the answer is not 325
To find the area of triangle ABC, we can use the formula for the area of a triangle:
Area = (1/2) * base * height
The base of the triangle is side AB, which has a length of length b = 65m.
To find the height, we can split the triangle into two right-angled triangles by drawing a perpendicular from angle C to side AB. Let's call the foot of the perpendicular D. Triangle ABC is now divided into two triangles: ACD and BCD.
Since triangle ACD is a right-angled triangle, we can use trigonometry to find the length of AC. We know that AC is the side opposite to angle C, so we can use the sine function:
sin(C) = opposite/hypotenuse
sin(86) = AD / AC
Rearranging the equation, we get:
AC = AD / sin(86)
To find the length of AD, we can use the cosine function in triangle ACD:
cos(C) = adjacent/hypotenuse
cos(86) = AD / AC
AD = AC * cos(86)
Now we have the length of AC, we can find the area of triangle ABC:
Area = (1/2) * base * height
= (1/2) * b * AC
= (1/2) * 65m * AC
As we have yet to find the value of AC, we cannot calculate the exact area of triangle ABC.
Please provide the necessary information or check if there is any additional information available to find the length of AC.