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

Answer 1

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.