A 2m long ladder leaning against a wall makes an angle of 38 degrees with the wall. how far is the base of the ladder from the wall?
Recall your basic trig function definitions, in terms of the sides of a right triangle. In this case,
x/2 = sin 38°
To find the distance between the base of the ladder and the wall, we can use trigonometry. The given information is the length of the ladder (2m) and the angle it makes with the wall (38 degrees). We need to find the distance between the base of the ladder and the wall, which we can call "x".
In this case, the ladder acts as the hypotenuse of a right triangle, with the wall acting as one of the legs and the ground acting as the other leg. We can use the trigonometric function cosine (cos) to calculate the distance (x).
The cosine function is defined as the adjacent side divided by the hypotenuse. In our scenario, the adjacent side is the distance between the base of the ladder and the wall (x), and the hypotenuse is the length of the ladder (2m).
So, we have:
cos(angle) = adjacent side / hypotenuse
Plugging in the known values:
cos(38 degrees) = x / 2m
To solve for x, we need to rearrange the equation:
x = cos(38 degrees) * 2m
Now, we can calculate the value of x:
x ≈ cos(38 degrees) * 2m
Using a scientific calculator or trigonometric table, we find that cos(38 degrees) is approximately 0.7880. So, plugging that in:
x ≈ 0.7880 * 2m
x ≈ 1.576m
Therefore, the base of the ladder is approximately 1.576 meters away from the wall.