if the area of △ABC=92.5 Km^2, ∠C=73 degrees, abd b=16 km, then what is the length of a to the nearest km
To find the length of side a, we can use the formula for the area of a triangle:
Area = (1/2) * base * height
Since ∠C is 73 degrees, side c is opposite to angle C, and side b is adjacent to angle C, we can use the sine function to find the height of the triangle:
sin(∠C) = opposite / hypotenuse
sin(73) = height / 16
height = sin(73) * 16
To find the length of side a, we can use the Pythagorean theorem:
a^2 = c^2 - b^2
a^2 = (height)^2 + (b)^2
Substituting the values from above, we get:
a^2 = (sin(73) * 16)^2 + 16^2
a^2 = (0.9612617 * 16)^2 + 256
a^2 = (15.380188)^2 + 256
a^2 = 237.0222 + 256
a^2 = 493.0222
Taking the square root of both sides, we get:
a = √493.0222
a ≈ 22.19 km
Rounded to the nearest kilometer, the length of side a is 22 km.