if a 30 ft ladder makes a 65 degree angle with the ground, how many fee up the wall will it reach

To find out how far up the wall the ladder will reach, we can use trigonometry. Given that the ladder makes a 65-degree angle with the ground and has a length of 30 ft, we are looking for the height of the wall (opposite side).

Let's use the sine function:

sin(angle) = opposite/hypotenuse

sin(65) = height of the wall/30ft

Rearranging the equation, we have:

height of the wall = sin(65) * 30ft

Using a calculator, we can find:

height of the wall ≈ 27.54 ft

Therefore, the ladder will reach approximately 27.54 feet up the wall.

To determine how many feet up the wall a 30 ft ladder will reach when it makes a 65-degree angle with the ground, you can use trigonometry.

The ladder forms a right triangle with the wall, with the ladder as the hypotenuse and the distance up the wall as the opposite side.

Using the trigonometric function sine (sin), you can find the ratio between the opposite side and the hypotenuse:

sin(angle) = opposite / hypotenuse

In this case, the angle is 65 degrees and the hypotenuse (ladder) is 30 ft. We can rearrange the equation to solve for the opposite side:

opposite = sin(angle) * hypotenuse

Now we can plug in the values:

opposite = sin(65) * 30

To calculate this, you can use a calculator or math software that supports trigonometric functions. The result will give you the distance up the wall the ladder will reach.

height/30 = sin 65

height = 30sin65°
= .....