a ladder 10 m long just reaches the top of a vertical wall . if the ladder makes an angle of 60 degree with the wall , then find the height of wall .

15√3/2

To find the height of the wall, you can use trigonometry, specifically the sine function. Here's how to proceed:

Let's label the height of the wall as "h".

We know that the ladder forms a right triangle with the wall. The ladder is the hypotenuse, and the height of the wall is one of the sides.

Since we have the length of the ladder and the angle it forms with the wall, we can use the sine function:

sine(angle) = opposite/hypotenuse

In this case, the angle is 60 degrees and the hypotenuse is the length of the ladder, which is 10 meters.

So, we have:

sine(60) = h/10

Now, let's solve for h:

h = 10 * sine(60)

Using a scientific calculator, you can find that the sine of 60 degrees is equal to √3/2. Plugging in that value, we get:

h = 10 * (√3/2)

Simplifying further, we have:

h = 5√3 meters

Therefore, the height of the wall is 5√3 meters.

sin30° = height/10

height = 10sin30
= ...