myxkeyisstuckxxxx
New Coder
We know that:
x = a = sin(θ) = y/z
y = b = cos(θ) = x/z
z = c = tan(θ) = y/x
This is very well known and it is sometimes simplified by the word sOHcAHtOA.
Now, how do we find the value of these variables using an alternative method? Well, we can use the following formulas:
x = sqrt(z^2 - y^2)
y = sqrt(z^2 - x^2)
z = sqrt(x^2 + y^2)
Here is an example:
A triangle with its hypotenuse measuring 10 units, its opposite measuring 4 units, and its adjacent measuring x units. What the value of x?
The variables are equal to:
y = 4
z = 10
The value of x is equal to:
x = sqrt(z^2 - y^2)
x = sqrt(10^2 - 4^2)
x = sqrt(84)
x = 9
We can verify it by doing:
z = sqrt(x^2 + y^2)
z = sqrt(9^2 + 4^2)
z = sqrt(97)
z = 10
And then for the value of y
The value of x is equal to:
y = sqrt(z^2 - x^2)
y = sqrt(10^2 - 9^2)
y = sqrt(19)
y = 4
We can verify it by doing:
z = sqrt(x^2 + y^2)
z = sqrt(9^2 + 4^2)
z = sqrt(97)
z = 10
And lastly, for the value of z, which is simply just the usual Pythagorean Theorem we all know and love.
Is there an existing method similar to this?
And, is this correct?
x = a = sin(θ) = y/z
y = b = cos(θ) = x/z
z = c = tan(θ) = y/x
This is very well known and it is sometimes simplified by the word sOHcAHtOA.
Now, how do we find the value of these variables using an alternative method? Well, we can use the following formulas:
x = sqrt(z^2 - y^2)
y = sqrt(z^2 - x^2)
z = sqrt(x^2 + y^2)
Here is an example:
A triangle with its hypotenuse measuring 10 units, its opposite measuring 4 units, and its adjacent measuring x units. What the value of x?
The variables are equal to:
y = 4
z = 10
The value of x is equal to:
x = sqrt(z^2 - y^2)
x = sqrt(10^2 - 4^2)
x = sqrt(84)
x = 9
We can verify it by doing:
z = sqrt(x^2 + y^2)
z = sqrt(9^2 + 4^2)
z = sqrt(97)
z = 10
And then for the value of y
The value of x is equal to:
y = sqrt(z^2 - x^2)
y = sqrt(10^2 - 9^2)
y = sqrt(19)
y = 4
We can verify it by doing:
z = sqrt(x^2 + y^2)
z = sqrt(9^2 + 4^2)
z = sqrt(97)
z = 10
And lastly, for the value of z, which is simply just the usual Pythagorean Theorem we all know and love.
Is there an existing method similar to this?
And, is this correct?