A ladder of length 5.8m is placed against the wall so that the foot of the ladder is 3.6m from the wall. Calculate the angle the ladder makes with the ground
What is the answer
The ladder forms a right triangle with the wall, where the floor and the wall form the legs, and the ladder is the hypotenuse.
Let the angle ladder makes with the floor be x.
Then by definition of the ratio cosine,
cosine(x)=adjacent side (floor)/hypotenuse
=3.6/5.8
On the calculator, use the inverse function acos, or cos-1to find the value of x, i.e.
x=acos(3.6/5.8)
Do not forget the parentheses around 3.6/5.8, else the answer will not be correct.
What the answer after that
Let me know
I don't know but I will use angle of elevation and depression by using SOH CAH TOA
Well, let's analyze this situation and see if we can climb the mathematical ladder together!
So, we have a ladder that is 5.8 meters long, leaning against a wall. The foot of the ladder is 3.6 meters away from the wall. To find the angle that the ladder makes with the ground, we need to use a little thing called trigonometry.
Now, let's introduce a little friend called the Pythagorean theorem. According to it, the square of the hypotenuse (the ladder) is equal to the sum of the squares of the other two sides (the distance from the foot of the ladder to the wall and the distance from the foot of the ladder to the top of the ladder).
Mathematically, we have:
h^2 = x^2 + y^2
Where h is the length of the ladder, x is the distance from the foot of the ladder to the wall (3.6), and y is the distance from the foot of the ladder to the top of the ladder (our mysterious angle).
Plugging in the given values, we have:
5.8^2 = 3.6^2 + y^2
Now, let's solve for y, or our mysterious angle.
y^2 = 5.8^2 - 3.6^2
y^2 = 33.64 - 12.96
y^2 = 20.68
y ≈ √20.68
y ≈ 4.55
Now that we know the length of the side opposite to our angle, we can finally use some arc functions to find the angle itself. More specifically, we'll use the arctangent function (tan^-1(y/x)).
tan^-1(4.55/3.6) ≈ 52.06°
So, the ladder makes an angle of approximately 52.06 degrees with the ground.
Remember, math can be a bit of a balancing act sometimes, but with a little humor and determination, we can always find our way to the answer!
To calculate the angle the ladder makes with the ground, we can use trigonometry. Specifically, we can use the sine function.
The ladder, the wall, and the ground form a right triangle. The ladder is the hypotenuse of the triangle, and the distance from the wall to the foot of the ladder is one of the legs.
Let's call the angle between the ladder and the ground θ. We can use the sine function to relate the angle θ to the sides of the triangle:
sin(θ) = opposite/hypotenuse
In this case, the opposite side is the distance from the wall to the foot of the ladder, which is 3.6m, and the hypotenuse is the length of the ladder, which is 5.8m.
Plugging the values into the equation, we get:
sin(θ) = 3.6/5.8
To find the angle θ, we can take the inverse sine (also called arcsine) of both sides of the equation:
θ = arcsin(3.6/5.8)
Using a calculator or a trigonometric table, we can determine the value of arcsin(3.6/5.8) as approximately 38.75 degrees.
Therefore, the angle the ladder makes with the ground is approximately 38.75 degrees.