A 6m ladder is leaning against a wall. The base of the ladder is 1.5m from the wall. Calculate the angle (to the nearest tenth) formed between the ladder and the ground.
To calculate the angle formed between the ladder and the ground, we can use trigonometry. In this case, we can use the tangent function.
The tangent function is defined as the ratio of the opposite side to the adjacent side of a right triangle. In this scenario, the opposite side is the height of the ladder against the wall, and the adjacent side is the distance from the base of the ladder to the wall.
By rearranging the formula for tangent, we can calculate the angle:
angle = arctan(opposite / adjacent)
In this case, the opposite side is the height of the ladder, which is 6 meters, and the adjacent side is the distance from the base of the ladder to the wall, which is 1.5 meters.
Plugging these values into the formula:
angle = arctan(6 / 1.5)
Using a calculator, we can evaluate the arctan function to find the angle:
angle ≈ arctan(4)
The angle to the nearest tenth is approximately 75.96 degrees.
Therefore, the angle formed between the ladder and the ground is approximately 75.96 degrees.
review your basic trig functions.
Draw a diagram, and you can easily see that
cosθ = 1.5/6