A ladder 5m lng leans against the warll so that it makes an angle of 60 with the horizontal ground . calculate how far the wll the ladder reaches
I don't even know
surely you have studied the special 30-60-90 triangle.
The sides are in the ratio 1:√3:2
So, in this triangle, the sides are 5/2 : 5√3/2 : 5
To calculate how far the ladder reaches up the wall, we need to use trigonometry. In this case, we can use the sine ratio.
The sine ratio states that the sine of an angle in a right triangle is equal to the length of the side opposite the angle divided by the length of the hypotenuse. In our case, the angle is 60 degrees, the side opposite the angle is the height of the wall, and the hypotenuse is the length of the ladder.
Given that the ladder is 5m long and the angle with the ground is 60 degrees, we need to solve for the height of the wall.
Step 1: Convert the angle from degrees to radians.
The equation for converting degrees to radians is: Radians = Degrees * (π / 180)
So, 60 degrees in radians would be: 60 * (π / 180) ≈ 1.05 radians.
Step 2: Use the sine ratio to find the height of the wall.
sin(θ) = height / length
sin(1.05) = height / 5
Step 3: Solve for the height.
height = sin(1.05) * 5
Using a calculator, we can find the value of sin(1.05) to be approximately 0.866.
Thus, height = 0.866 * 5 ≈ 4.33 m.
Therefore, the ladder reaches a height of approximately 4.33 meters up the wall.