A ladder is resting against a wall. The ladder and the ground and angle of 40 degrees and the ladder is 4 ft. from the wall. How long is the ladder?
if the ladder has length x,
4/x = cos 40°
x = 5.22 ft
To find the length of the ladder, we can use trigonometry. In this case, we can use the sine function.
The sine of an angle in a right triangle can be calculated by dividing the length of the side opposite the angle by the length of the hypotenuse.
In this scenario, the ladder is the hypotenuse of the triangle, and the distance from the wall is the opposite side. Let's call the length of the ladder "L" and the distance from the wall "d".
Using the formula of sine:
sin(angle) = opposite / hypotenuse
sin(40 degrees) = d / L
Since we know the angle (40 degrees) and the distance from the wall (4 ft), we can rearrange the equation to solve for "L":
L = d / sin(angle)
L = 4 ft / sin(40 degrees)
Using a calculator, we can find the sine value of 40 degrees:
sin(40 degrees) ≈ 0.643
Now we can substitute this value into the equation to find "L":
L = 4 ft / 0.643 ≈ 6.22 ft
Therefore, the length of the ladder is approximately 6.22 ft.