if a wall is 34 feet, how tall must a ladder be to reach the top if at a 75 degree angle

let x = length of ladder

if you draw the figure, you actually form a right triangle, where the ladder is the hypotenuse, and the wall is the height. Thus, we use trigonometry.
sin (angle) = opposite / hypotenuse
sin 75 = 34 / x
x = 34 / (sin 75)
x = 34 / 0.966
x = 37.27 ft

hope this helps~ :)

To determine the height of the ladder needed to reach the top of a wall at a 75-degree angle, we can use trigonometry.

In this case, we have a right triangle formed by the wall, the ground, and the ladder. The length of the ladder represents the hypotenuse, and the angle between the wall and the ground (75 degrees) will be used to find the height of the ladder.

To find the height, we can use the sine function, which relates the length of the side opposite the angle to the length of the hypotenuse. The formula is:

sin(angle) = opposite / hypotenuse

Rearranging the formula to solve for the opposite side (height in this case), we have:

height = sin(angle) * hypotenuse

Since we know the angle (75 degrees) and the length of the wall (34 feet), we can calculate the height as follows:

height = sin(75 degrees) * 34 feet

To calculate the value, we can input these values into a scientific calculator or use an online trigonometric calculator. The result will give you the height of the ladder required to reach the top of the wall.