To calculate the height of the pole, we can use the tangent of the angle between the ground and the pole.The tangent of the angle of 45° is the opposite side (the height of the pole) divided by the adjacent side (the distance from the pole to the observer).The tangent of the angle of 60° is the opposite side (the height of the pole) divided by the adjacent side (the distance from the pole to the observer plus 10m).We can use these two equations to set up a system of equations and solve for the height of the pole:tan(45°) = h / xtan(60°) = h / (x + 10)Where h is the height of the pole and x is the distance from the pole to the observer.By solving this system of equations, we get: h = (x * tan(60°)) + (10 * tan(45°))Since we know that x = 10m, we can substitute that value into the equation and get:h = (10 * tan(60°)) + (10 * tan(45°))h = 14.14213562373095The height of the pole is approximately 14.14 meters.