Final answer:
The height at which the 14-foot ladder reaches up the building, when it makes a 56° angle with the ground, is approximately 11.6 feet.
Step-by-step explanation:
To solve how high up the building the ladder reaches, we will use trigonometry, specifically the sine function, as we are dealing with a right triangle where we know the angle the ladder makes with the ground and the hypotenuse (the ladder's length). The sine of an angle in a right triangle equals the opposite side (height, in this case) over the hypotenuse (the ladder's length).
The sine of 56° is (≈ 0.8290). So the equation we will use is:
sin(56°) = Height / 14 feet
Therefore, to find the height:
Height = 14 feet * sin(56°)
Which is approximately:
Height = 14 feet * 0.8290
Height = 11.606 feet, rounded to the nearest tenth, is 11.6 feet.
This is the height the ladder reaches up the building.