A 12' ladder leans against a wall at 68 degree angle of elevation. Find the distance from the ladder's base to the wall.
or, using this equation
x/12 = cos 68° = 0.374
x = 4.46
The answer is the same anyway :)
To find the distance from the ladder's base to the wall, we can use trigonometry. Let's call the distance from the ladder's base to the wall "x".
We know that the ladder forms a right-angled triangle with the wall, where the ladder is the hypotenuse and the distance from the base to the wall is the adjacent side.
In this case, the angle of elevation of the ladder is 68 degrees, which means that the adjacent side is x and the hypotenuse is 12 feet.
Using the cosine function, we have:
cos(θ) = adjacent/hypotenuse
cos(68) = x/12
To solve for x, we can rearrange the equation:
x = cos(68) * 12
Using a calculator, we find:
x ≈ 4.80 feet
Therefore, the distance from the ladder's base to the wall is approximately 4.80 feet.
Hi Ruth,this is easy!
Imagine a right angle triangle. In this case, the length of the hypothenuse is 12'.Given the angle of elevation 68 degrees. Since it is a right angle triangle,one of the remaining two angles is 90 degrees. So the third angle is 180-90-68 = 22 degrees.
Now we know the angles and we know the length of hypothenuse is 12'. We need to find the distance of ladder's base to the wall. Since two angles and a length is known, we have to use sine formula:
a / sin A = b / sin B
Let a = 12' therefore sin A is sin 90 degrees since it is opposite to the hypothenuse. Let b be the distance needed to be found. So sin B is sin 22 degrees since it is opposite to b.
The answer is b = 4.5'