A ladder leans against a building, forming an angle of 53° with the ground. The base of the ladder is 3 ft from the building. To the nearest hundredth of a foot, how long is the ladder?
length of ladder --- x
cos 5° = 3/x
x = 3/cos53 = .....
sticky key, should have said
cos 53° = 3/x
To find the length of the ladder, we can use trigonometry. Let's call the length of the ladder "L". We have the information that the base of the ladder (the distance from the building) is 3 feet and the angle between the ladder and the ground is 53 degrees.
We can use the sine function since we know the opposite side (the height of the ladder) and the hypotenuse (length of the ladder).
The sine of an angle is defined as the length of the opposite side divided by the length of the hypotenuse. So we can write:
sin(53°) = Opposite / Hypotenuse
We can rearrange this equation to solve for L:
L = Opposite / sin(53°)
The opposite side of the angle is the height of the ladder. We can use trigonometry again to find it. Since the base of the ladder is 3 feet, we can use the cosine function:
cos(53°) = Adjacent / Hypotenuse
Rearranging this equation:
Adjacent = cos(53°) * Hypotenuse
Adjacent in this case represents the distance between the building and the ladder. We know this distance is 3 feet, so we can substitute it:
3 ft = cos(53°) * Hypotenuse
Now we can solve for the hypotenuse:
Hypotenuse = 3 ft / cos(53°)
Finally, substitute this value into the previous equation for L:
L = (3 ft) / cos(53°) / sin(53°)
Using a calculator, we get:
L ≈ 5.62 ft
Therefore, the length of the ladder is approximately 5.62 feet.