a 3.8m ladder rests against a vertical wall and makes an angle of 38 degrees with the wall. how far does the ladder reach up the wall?
cos 38 = h/3.8
To find how far the ladder reaches up the wall, we need to use trigonometry, specifically the concept of sine. The sine function relates the length of the side opposite an angle to the length of the hypotenuse.
In this case, the ladder forms a right triangle with the wall, where the ladder is the hypotenuse and the distance it reaches up the wall is the opposite side. The angle formed by the ladder with the wall is given as 38 degrees.
To find the distance the ladder reaches up the wall, we can use the formula:
Opposite = Hypotenuse * sin(Angle)
Here:
Hypotenuse = 3.8 meters (length of the ladder)
Angle = 38 degrees
Now, let's calculate the magnitude of the distance:
Opposite = 3.8 meters * sin(38 degrees)
Opposite = 3.8 meters * 0.6157
Opposite ≈ 2.33 meters
So, the ladder reaches approximately 2.33 meters up the wall.