if the area of triangle ABC equals 92.5 KM squared angle C equals 76° and B equals 16 KM then what is the length of a to the nearest KM
To find the length of side a of triangle ABC, we can use the formula for the area of a triangle:
Area = 1/2 * base * height
In this case, the base of the triangle is side b (16 km) and the height can be calculated using the formula:
height = base * sin(angle C)
height = 16 * sin(76°)
height ≈ 15.74 km
Now, we can plug in the values into the formula for the area of the triangle:
92.5 = 1/2 * 16 * 15.74
92.5 = 8 * 15.74
92.5 = 125.92
Now we can solve for side a:
125.92 = 1/2 * a * 15.74
125.92 = 7.87a
a ≈ 125.92 / 7.87
a ≈ 16 km
Therefore, the length of side a of triangle ABC is approximately 16 km.