a laddder 9m long rests against a vertical wall. if the base of the ladder is 2m from the wall, find the angle mabe by the ladeer with the ground

Cos A = 2m/9m.

99.2 brikes

To find the angle made by the ladder with the ground, we can use the trigonometric function of sine.

Let's consider the ladder as the hypotenuse of a right-angled triangle, with the vertical wall as one of the sides and the distance from the base of the ladder to the wall as the other side.

According to the problem, the ladder is 9 meters long, and the base of the ladder is 2 meters from the wall. So, we have the following information:
- Length of the ladder (hypotenuse) = 9m
- Distance from the base of the ladder to the wall (adjacent side) = 2m

Using the formula for sine:

sin(angle) = opposite/hypotenuse

In this case, the opposite side is the distance from the base of the ladder to the wall. However, we don't have this information.

To find the opposite side, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides:

hypotenuse^2 = adjacent^2 + opposite^2

Therefore, we can calculate the opposite side as follows:

opposite^2 = hypotenuse^2 - adjacent^2
opposite^2 = 9^2 - 2^2
opposite^2 = 81 - 4
opposite^2 = 77

Taking the square root of both sides:
opposite ≈ √77

Now that we know the opposite side, we can find the angle by using the formula for sine:

sin(angle) = opposite/hypotenuse
sin(angle) = (√77) / 9

Finally, we can find the angle by taking the inverse sine (arcsine) of both sides:

angle ≈ arcsin((√77) / 9)

Using a calculator, the approximate value of the angle is 11.4 degrees.