A 15 ft. ladder is leaning against the side of a house and forms an angle of 66o with the ground. To the nearest foot how far from the base house is the foot of the ladder?
I set it up cos66=15/x
15/cos66 =36.878, rounding to the nearest ft makes it 37
It doesn't sound right when you have a 15 ft. ladder leaning against a wall with the foot of the ladder 36.9 ft away.
So you need to recheck your work when it does not look right.
The length of the ladder is the hypotenuse of the right triangle.
The base of the ladder is adjacent to the 66° angle, so by definition of cosine,
Distance from the wall
= hypotenuse * cos(66°)
= 15 cos(66°)
= 6.1 ft approximately.
To find the distance from the base of the ladder to the foot of the ladder, you can use trigonometry.
First, you can set up a right triangle with the ladder as the hypotenuse, the distance from the base of the ladder to the foot as the adjacent side, and the vertical height (height of the house) as the opposite side.
In this case, you know the length of the ladder (hypotenuse) is 15 ft, and the angle between the ladder and the ground is 66 degrees.
You can use the cosine function to find the adjacent side, which represents the distance from the base of the ladder to the foot.
cos(angle) = adjacent/hypotenuse
cos(66 degrees) = adjacent/15 ft
To solve for the adjacent side, you can rearrange the equation:
adjacent = cos(66 degrees) * 15 ft
Using a calculator, you can find the value of cos(66 degrees) is approximately 0.4067.
Now you can substitute this value into the equation:
adjacent = 0.4067 * 15 ft
adjacent ≈ 6.1005 ft
Rounding to the nearest foot gives us 6 feet. So, the foot of the ladder is approximately 6 feet from the base of the house.