3. A ladder leaning against a wall makes a angle with the ground. The base of the ladder is 4 meters from the building. How high above the ground is the top of the ladder?
How long is the ladder?
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To find the height of the ladder, we can use trigonometry. First, let's define the given information:
Let "a" be the angle made by the ladder with the ground.
Let "b" be the distance between the base of the ladder and the building, which is 4 meters.
Let "c" be the height of the ladder, which is the distance from the ground to the top of the ladder.
We are looking to find the value of "c".
Now, we can use the trigonometric function tangent (tan) to solve for "c". The tangent of an angle is defined as the ratio of the opposite side to the adjacent side of a right triangle.
In this case, the height of the ladder is the opposite side and the distance between the base and the building is the adjacent side.
Using the tangent function, we have:
tan(a) = c / b
Rearranging the equation, we get:
c = b * tan(a)
Substituting the given values, we have:
c = 4 * tan(a)
To find the height, we need to know the angle "a". The question does not provide the angle, so we cannot calculate the exact height without that information.