A 6 m ladder is leaning against the wall of a house

The angle between the ladder and the ground
Is 60 degrees . How far away is the ladder from
the wall? How high up the house does the ladder
reach? Give your answers accurate to two decimal places

you should know that the sides of a 30-60-90 triangle are in the ratio 1:√3:2

so, the triangle formed by your ladder has sides

3:3√2:6

To find the distance the ladder is from the wall, we can use trigonometry. In this case, we can use the sine function.

Let's denote the distance the ladder is from the wall as x.

Using the sine function, we have:

sin(60 degrees) = opposite/hypotenuse
sin(60 degrees) = x/6

To find x, we can rearrange the equation:

x = sin(60 degrees) * 6

Calculating this:

x = 0.866 * 6 ≈ 5.20 meters

Therefore, the ladder is approximately 5.20 meters away from the wall.

Now, let's find out how high up the ladder reaches on the house.

Using the same triangle formed by the ladder, ground, and the height on the house, we can again use the trigonometric functions. In this case, we can use the cosine function.

Using the cosine function, we have:

cos(60 degrees) = adjacent/hypotenuse
cos(60 degrees) = height/6

To find the height, we can rearrange the equation:

height = cos(60 degrees) * 6

Calculating this:

height = 0.5 * 6 = 3 meters

Therefore, the ladder reaches a height of approximately 3 meters up the house.