Question

a 14 foot ladder is leaning against a building the ladder makes a 45 degree angle with the building how far up the building does the ladder reach

Answer 1

Ladder reaches 9.9 feet

Explanation:

To find how far up the building the ladder reaches, you can use trigonometry. The ladder, the building, and the ground form a right triangle. The ladder is the hypotenuse, and the angle between the ladder and the ground is 45 degrees.

Using the trigonometric function sine (sin), we can find the height (h) the ladder reaches on the building:

sin(45 degrees) = opposite / hypotenuse

Since the opposite side is the height (h) we want to find and the hypotenuse is the length of the ladder (14 feet):

h = 14 feet * sin(45 degrees)

Now, let's calculate the value:

h ≈ 14 feet * 0.7071 ≈ 9.9 feet

So, the ladder reaches approximately 9.9 feet up the building.