D.) A 20-ft ladder leans against a house and the base
of the ladder is 5 feet from the base of the house.
What is the angle formed by the ladder and the
ground?

The angle formed equals 75.5.

Step-by-step explanation: Please refer to the attached diagram.

If a ladder leans against a wall, it would form a diagonal since the wall is a vertical line (that is, straight from top to bottom). As shown in the diagram attached, the ladder leaning against a wall would form a right angled triangle ABC. Side AB is the ladder and side AC is the wall while side BC is the distance from the base of the ladder to the base of the wall.

When the ladder tilts forward and touches the wall at point A, it forms an angle at point B {which has been marked as X}. To compute the size of the angle X, we shall use trigonometric ratios. Side AB is the hypotenuse (line facing the right angle). Side BC is the adjacent (side which lies between the reference angle and the right angle). Having identified the adjacent and the hypotenuse, we can now calculate using the ratio of Cosine.

Cos X = Adjacent/Hypotenuse

Cos X = BC/AC

Cos X = 5/20

Cos X = 1/4

(Converting our fraction into a decimal, 1/4 = 0.25)

Cos X = 0.25

By checking with a calculator or referring to a table of values, 0.25 equals 75.52. Approximately that equals 75.5 degrees.

5+2x=a

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