Explanation
The Pythagorean theorem is a key principle in Euclidean geometry. It states that the square of the longest side of a right triangle (the hypotenuse) is equal to the sum of the squares of the other two sides. The theorem is written as an equation like this:
a 2 + b 2 = c 2
When any two sides are know, this equation can be used to solve for the third side. When a and b are known, the length of the hypotenuse can be calculated with:
When b and c are known, the length of side a can be calculated with:
When a and c are known, length of side b can be calculated with:
To translate the above into Excel formula syntax, use the exponentiation operator (^) and the SQRT function , as seen below. The Pythagorean theorem can be written as:
=a^2+b^2=c^2 // Pythagorean theorem
And the formulas below can be used to solve for each of the three sides:
c=SQRT(a^2+b^2) // hypotenuse
a=SQRT(c^2-b^2) // side a
b=SQRT(c^2-a^2) // side b
Instead of the exponentiation operator, you can also use the POWER function like this:
c=SQRT(POWER(a,2)+POWER(b,2))
a=SQRT(POWER(c,2)-POWER(b,2))
b=SQRT(POWER(c,2)-POWER(a,2))
The formulas above are an example of nesting one function inside another.
Explanation
In geometry, the formula for calculating the surface area of a right cone is:
The Greek letter π (“pi”) represents the ratio of the circumference of a circle to its diameter. In Excel, π is represented in a formula with the PI function , which returns the number 3.14159265358979, accurate to 15 digits:
=PI() // returns 3.14159265358979
To square a number in Excel, you can use the exponentiation operator (^):
=A1^2
To get the square root of a number, you can use the SQRT function :
=SQRT(A1)
Rewriting the formula for surface area of a cone with Excel’s math operators , we get:
=PI()*B5*(B5+SQRT(C5^2+B5^2))
Following Excel’s order of operations , exponentiation will occur before multiplication.
