Question

A ladder leans against the wall of a building. The ladder measures

41 inches and forms an angle of 42° with the ground. How far from
the ground, in inches, is the top of the ladder? How far from the
wall, in inches, is the base of the ladder? Round to two decimal
places as needed.

Answer 1

We can use trigonometry to solve this problem. Let's call the height of the ladder "h" and the distance from the wall to the base of the ladder "d".

From the problem, we know that the ladder forms a 42° angle with the ground. This means that the sine of the angle is equal to the opposite side (h) over the hypotenuse (41 inches):

sin(42°) = h/41

We can solve for h by multiplying both sides by 41 and taking the sine of 42°:

h = 41 × sin(42°)

h ≈ 28.61 inches

So the top of the ladder is about 28.61 inches from the ground.

To find the distance from the wall to the base of the ladder, we can use the cosine of the angle:

cos(42°) = d/41

We can solve for d by multiplying both sides by 41 and taking the cosine of 42°:

d = 41 × cos(42°)

d ≈ 31.15 inches

So the base of the ladder is about 31.15 inches from the wall.