a 4-m plank rests against a wall 1.8m high so that 1.2m of it projects beyond the wall. find the angle the plank makes with wall.
To find the angle the plank makes with the wall, we need to use the trigonometric function tangent.
Let's label the length of the part of the plank that is against the wall as "a" and the length of the part that is projecting beyond the wall as "b."
From the information given, we know that a = 1.8m (the height of the wall) and b = 1.2m (the part projecting beyond the wall).
Using the tangent function, we can write:
tan(angle) = opposite / adjacent
In this case, the opposite side is the part projecting beyond the wall (b) and the adjacent side is the part against the wall (a).
So, we have:
tan(angle) = b / a
Plugging in the values we know:
tan(angle) = 1.2m / 1.8m
Now, to find the angle, we need to take the inverse tangent (arctan) of both sides:
angle = arctan(1.2m / 1.8m)
Using a calculator or a trigonometric table, we calculate the arctan(1.2m / 1.8m) to find the angle.
So, the angle the plank makes with the wall is the value we obtain from the arctangent function.