A 12-foot ladder that is leaning against a wall makes a angle with the level ground.
What equation can be used to determine the height in feet (y) from the ground to where the ladder touches the wall?
You will have to have more information, such as,
what is the size of the angle,
or,
how far from the wall is the foot of the ladder.
To determine the height in feet (y) from the ground to where the ladder touches the wall, you can use trigonometry. In this case, we have a right triangle formed by the ladder, the wall, and the ground. The angle formed between the ladder and the ground is given as θ.
In trigonometry, the sine function relates the lengths of the sides of a right triangle to the angles. In this case, the sine of θ is defined as the ratio of the opposite side (which is y, the height of the ladder from the ground) to the hypotenuse (which is the length of the ladder, 12 feet).
Therefore, the equation to determine the height (y) is:
sin(θ) = y / 12
To solve for y, you need to know the value of the angle θ. Once you have that, you can rearrange the equation to solve for y.
Note: In order to work with angles in trigonometry, they are most commonly measured in radians, not degrees. If you have the angle measured in degrees, you will need to convert it to radians before using the equation.