A right triangle has a hypotenuse = 39 cm and a side = 15 cm. What is the third side?

2 Answers
May 15, 2018

The third side is 36 cm long.

Explanation:

Consider a the side of 15 cm, b the unknown side and c the hypotenuse. Use pythagoras' theorem and plug in all your values, Solve for b.

#a^2 + b^2 = c^2 #
#b^2 = c^2 - a^2#
#b^2 = 39^2 - 15^2#
#b^2 = 1521 - 225 #
# b^2 = 1296#
# b = sqrt1296 #
# b= 36#

May 15, 2018

36 cm

Explanation:

In a right triangle, we know using Pythagorean Theorem that #a^2+b^2=c^2# where c is the hypotenuse, and a and b are the two other sides.

In this example, #c=39#, and one of the sides (since the two sides are interchangeable, let's just assume it's a) #=15#

Inputting this value into the equation gives us #15^2+b^2=39^2#.
Subtracting #15^2# from each side gives us #b^2=39^2-15^2#
Solving for b gives us #b=sqrt(39^2-15^2)#

If you have a calculator with you, you could simply input values.
If not, you could use simple multiplication and subtraction or some factoring methods.

Either way, the answer is #b=36#, so the length of the missing side is 36 cm.