The lengths of two sides of a right angled triangle are 20 cm and 30 cm. Calculate the length of the third side, if it is:
(a) the hypotenuse
(b) not the hypotenuse

Answers:

Those values are exact. They approximate to:

10*sqrt(13) = 36.0555

10*sqrt(5) = 22.3607

Explanation:

Part (a)

If the unknown third side is the hypotenuse then we need to find the value of c when a = 20 and b = 30.

Apply the pythagorean theorem

a^2 + b^2 = c^2

20^2 + 30^2 = c^2

400 + 900 = c^2

1300 = c^2

c^2 = 1300

c = sqrt(1300)

c = sqrt(100*13)

c = sqrt(100)*sqrt(13)

c = 10*sqrt(13)   exact length

c = 36.0555 approximate length

Part (b)

If the third side is not the hypotenuse then that must mean c = 30 is the hypotenuse as this side is larger than the 20 cm side. The hypotenuse is always the longest side.

Let a = 20 be the known leg. Let's find the other unknown leg b using the pythagorean theorem.

a^2 + b^2 = c^2

20^2 + b^2 = 30^2

400 + b^2 = 900

b^2 = 900-400

b^2 = 500

b = sqrt(500)

b = sqrt(100*5)

b = sqrt(100)*sqrt(5)

b = 10*sqrt(5) exact length

b = 22.3607  approximate length

in mathematics, a function is a relationship between two variables such that the value of one of the variables, called the dependent variable, is determined by the value of the other variable, called the independent variable. there is a specific term we use to describe the set of independent variables of a function.

step-by-step explanation:

i think you should think about the question and not look online.