A 6m ladder leans against a wall. The foot of the ladder is placed at an angle of elevation at 63 degrees with the ground. How far is the foot of the ladder from the wall?
We dra a rt. triangle.
X = Hor. side = Dist. from foot of ladder to wall.
Y = Ver. side.
Z = Hyp. = 6 m. = Length of ladder.
X = Z*cos63 = 6*cos63 = 2.72 m.
Post it.
To find the distance between the foot of the ladder and the wall, we can use trigonometry. Let's label the distance we're trying to find as x.
In this problem, we have a right triangle formed by the ladder, the ground, and the wall. The angle between the ground and the ladder is given as 63 degrees.
Using trigonometry, we can use the sine function to relate the angle and the sides of the triangle. In this case, the side opposite the angle is the distance x between the foot of the ladder and the wall, and the hypotenuse is the length of the ladder, which is 6m.
The sine of an angle is equal to the ratio of the length of the side opposite the angle to the length of the hypotenuse. So we can write:
sin(63 degrees) = x/6
To find x, we need to solve for it. Rearranging the equation, we have:
x = 6 * sin(63 degrees)
Calculating this value, we get:
x ≈ 5.25 meters
Therefore, the foot of the ladder is approximately 5.25 meters away from the wall.