a 10 foot ladder is leaning against a wall at a 40 degree angle. how far up the wall does the ladder reach?
d = 10sin40 = 6.43 ft.
12.0
22.7
To determine how far up the wall the ladder reaches, you can use trigonometry specifically the trigonometric function sine (sin). The sine of an angle in a right triangle is equal to the opposite side divided by the hypotenuse.
In this case, the length of the ladder is the hypotenuse, and the height up the wall is the opposite side to the angle of 40 degrees. We need to find the height.
Given:
Angle (θ) = 40 degrees
Length of the ladder (hypotenuse) = 10 feet
First, convert the angle from degrees to radians since most programming languages use radians. To convert degrees to radians, use the formula:
radians = degrees * π / 180
So, for an angle of 40 degrees:
radians = 40 * π / 180
Now, calculate the height using the sine function:
height = length of ladder * sin(radians)
Plug in the values:
height = 10 * sin(radians)
Finally, calculate the value of the sine and solve for the height:
height = 10 * sin(40 * π / 180) ≈ 6.427 feet
Therefore, the ladder reaches approximately 6.427 feet up the wall.