A ladder is leaning against the side of a house and forms an angle of 66o with the ground. The foot of the ladder is 11.3 feet from the base of the house. Find the length of the ladder to the nearest foot.
how about
cos 66° = 11.3/L
L = 11.3/cos66 = appr 28 ft
thank you
To find the length of the ladder, we can use trigonometry.
In this scenario, the ladder forms a right triangle with the side of the house and the ground. The angle between the ladder and the ground is given as 66 degrees. We also know that the foot of the ladder is 11.3 feet away from the base of the house.
Let's call the length of the ladder "L". We can use the sine function to relate the angle, the opposite side (which is the height of the house), and the hypotenuse (which is the length of the ladder). The formula is:
sin(angle) = opposite / hypotenuse
In this case, angle = 66 degrees, opposite = height of the house, and hypotenuse = length of the ladder.
Rearranging the formula to solve for the hypotenuse, we have:
hypotenuse = opposite / sin(angle)
Now, we can substitute the given values into the formula:
hypotenuse = 11.3 feet / sin(66 degrees)
Using a calculator, we find:
hypotenuse ≈ 12.26 feet
Therefore, the length of the ladder to the nearest foot is 12 feet.