A 7-foot ladder is leaned against a building in such a way that the bottom of the ladder is 4 feet from the base of the wall. Find the angle formed between the ladder and the ground.

6.7

To find the angle formed between the ladder and the ground, we can use trigonometry. In this case, we can use the property of the tangent function.

We know that the height of the ladder is 7 feet and the base of the ladder is 4 feet. We can use these measurements to calculate the angle.

The tangent of an angle theta is defined as the ratio of the opposite side to the adjacent side. In this case, the opposite side is the height of the ladder and the adjacent side is the base of the ladder.

Let's denote the angle as theta. Then, we have:

tan(theta) = opposite/adjacent
tan(theta) = 7/4

To find the angle, we need to take the inverse tangent (arctan) of both sides:

theta = arctan(7/4)

Using a scientific calculator, we can evaluate this expression to find the angle.

Therefore, the angle formed between the ladder and the ground is approximately equal to arctan(7/4).

X = 4

r = 7 = hyp.

cos A = X/r = 4/7 = 0.57143
A = 55.15o

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