A 25-foot ladder leans against a house. The bottom of the ladder is 7 feet from the house.

To the nearest degree, what angle does the ladder make with the ground?

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It makes a 74 degree angle.

The sides of the triangle that are given are the side adjacent to the angle the ladder makes with the ground and the hypotenuse of the triangle.

adjacent/hypotenuse is the ratio for cosine:

cos x = 7/25

To solve this, we will take the inverse cosine:

x = cos⁻¹ (7/25) = 73.7 = 74