a ladder 15 meters long just reaches the top of a vertical wall. if the ladder makes an angle of 60 degrees with the wall. find the height of wall.....

7.5

To find the height of the wall, we can use trigonometry. In this case, we can use the trigonometric function sine (sin).

Let's define the given information:
Ladder length (l) = 15 meters
Angle between the ladder and the wall (θ) = 60 degrees

Since we are given the length of the ladder and the angle it makes with the wall, we can apply the sine function. The sine function relates the length of the side opposite the angle (the height of the wall) to the hypotenuse (the length of the ladder).

The formula to find the height of the wall using sine is:
sin(θ) = Opposite/Hypotenuse

Rearranging the formula to solve for the height of the wall (Opposite), we get:
Opposite = sin(θ) * Hypotenuse

Now, let's substitute the values into the formula:
Opposite = sin(60 degrees) * 15 meters

To evaluate sin(60 degrees), we can use a trigonometric table, calculator, or trigonometric identity.

For a 60-degree angle, sin(60 degrees) is equal to √3/2.

Substituting the value into the formula:
Opposite = (√3/2) * 15 meters

Calculating the result:
Opposite = (1.732/2) * 15 meters
Opposite = 0.866 * 15 meters
Opposite = 13 meters (rounded to the nearest whole number)

Therefore, the height of the wall is approximately 13 meters.

did you make a sketch?

if so, then you should see that
cos60° = height/15
height = 15cos60 = ...

BTW, that ladder is totally unsafe!!!!