A ladder is leaned 9m up a wall with its base 5m from the wall. What angle does the ladder make with the ground?
To find the angle that the ladder makes with the ground, we can use trigonometry. Specifically, we can use the tangent function.
The tangent of an angle can be defined as the ratio of the length of the opposite side to the length of the adjacent side. In this case, the opposite side is the height of the ladder on the wall (9m) and the adjacent side is the distance from the wall to the base of the ladder (5m).
Therefore, we can find the angle by taking the inverse tangent (or arctan) of the ratio of these two lengths:
angle = arctan(height/adjacent)
In this case, the angle would be:
angle = arctan(9/5)
To find the value of this angle, we can use a scientific calculator or an online calculator that has the arctan function. By plugging in the ratio of 9/5, the calculator will give us the angle in degrees.
The result is approximately 59.04 degrees (rounded to two decimal places).
Therefore, the ladder makes an angle of approximately 59.04 degrees with the ground.