Question

The 19.9 foot ladder leans against a wall from a point that 2.7 feet

away from the wall on the ground. What is the angle between the
ladder and the wall to the nearest tenth of the degree?

Answer 1

Answer: 5.7 degrees to the nearest tenth of a degree

Explanation:

We can use trigonometry to find the angle between the ladder and the wall. Let's call this angle θ. The ladder, the wall, and the ground form a right triangle, where the ladder is the hypotenuse, the wall is one leg, and the distance from the base of the ladder to the wall is the other leg.

Using the Pythagorean theorem, we can find the length of the ladder:

ladder^2 = wall^2 + distance^2

ladder^2 = (2.7)^2 + (19.9)^2

ladder^2 = 776.3

ladder = sqrt(776.3)

ladder ≈ 27.9 feet

Now we can use the sine function to find the value of the angle θ:

sin(θ) = opposite / hypotenuse

sin(θ) = wall / ladder

sin(θ) = 2.7 / 27.9

Taking the inverse sine (or arcsine) of both sides, we get:

θ = sin^(-1)(2.7 / 27.9)

Using a calculator, we find:

θ ≈ 5.7 degrees

Therefore, the angle between the ladder and the wall is approximately 5.7 degrees to the nearest tenth of a degree.