A triangular y field has two sides 60m and 75m long and the angle between them is 102m. how long is the third side?
Makes no sense, angles are not measure in metres.
If you meant degrees, then you have a clear case of the cosine law.
A10cmlong2cmwidewoodwedgeispushedintoasoftwoodblock.Calculate.The velocityratioofthe Wedgd
A10cmlong,2cmwidewoodwedgeispushedintoasoftwoodblock.Calculatd The Velocity Ratio Ofthewedge
To find the length of the third side of the triangular field, we can use the law of cosines. The law of cosines states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides, minus twice the product of the lengths of those sides multiplied by the cosine of the included angle.
Let's denote the lengths of the two given sides as a = 60m and b = 75m. The angle between them is C = 102 degrees.
Using the law of cosines, we can write:
c^2 = a^2 + b^2 - 2ab * cos(C)
Plugging in the known values:
c^2 = 60^2 + 75^2 - 2 * 60 * 75 * cos(102)
Now we can calculate the value of c:
c^2 = 3600 + 5625 - 2 * 60 * 75 * cos(102)
c^2 ≈ 3600 + 5625 - 2 * 60 * 75 * (-0.342020143)
c^2 ≈ 3600 + 5625 + 3723.603022
c^2 ≈ 12948.603022
Taking the square root of both sides, we find:
c ≈ √(12948.603022)
c ≈ 113.84
Therefore, the approximate length of the third side of the triangular field is 113.84 meters.