A pole 6m long leans against a vertical wall so that it makes an angle of 60 with the wall calculate the distance of the foot of the ladder from the wall.
cos 30 = x/6
x = 6 cos 30 = 5.2 m
Cos 30 =x/6
X=6 cos 30 =5.2 m
To calculate the distance of the foot of the ladder from the wall, we can use trigonometry. In this case, the ladder acts as the hypotenuse of a right triangle.
Let's label the distance of the foot of the ladder from the wall as "x". We also know that the length of the pole is 6m and it makes an angle of 60 degrees with the wall.
Using the cosine trigonometric function, we can write:
cos(60) = x/6
To find the value of cosine(60), we can use the unit circle or a calculator. The cosine of 60 degrees is equal to 0.5.
0.5 = x/6
Simplifying the equation, we can multiply both sides by 6:
6 * 0.5 = x
3 = x
Therefore, the distance of the foot of the ladder from the wall is 3 meters.
To solve this problem, we can use trigonometry.
Let's call the distance of the foot of the ladder from the wall "x". We can create a right triangle by drawing a perpendicular line from the foot of the ladder to the wall.
In this triangle, the length of the pole is the hypotenuse, which is 6m, and the angle between the pole and the wall is 60 degrees. We want to find the length of the side opposite to the angle (x), which represents the distance of the foot of the ladder from the wall.
Now, we can apply the trigonometric function "sin" to solve for x.
sin(60) = opposite/hypotenuse
sin(60) = x/6
Since sin(60) is equal to (√3)/2, we have:
(√3)/2 = x/6
To solve for x, we can cross multiply:
2x = 6 * (√3)
Divide both sides by 2:
x = 6 * (√3)/2
Simplify:
x = 3 * (√3)
Therefore, the distance of the foot of the ladder from the wall is 3 * (√3) meters.