A right triangle's leg is 9 and the hypotenuse is 15, what is the other leg s length?

2 Answers
Mar 31, 2017

Answer:

The length of the other leg is 12

Explanation:

The Pythagorean theorem is:

#a^2+b^2=c^2" [1]"#

Where "a" and "b" legs of the triangle and side "c" is the hypotenuse.

We are given that the triangles right leg is 9 and the hypotenuse is 51. Because addition is commutative, it does not matter whether we choose to assign "a" or "b" the known length; I shall choose "a":

Let #a = 9# and #c = 15#

Substitute this into equation [1]:

#9^2 + b^2 = 15^2#

Compute the squares:

#81+b^2=225#

Subtract 81 from both sides:

#b^2=144#

Square root both sides:

#b = +-12#

Discard the negative length:

#b = 12#

The length of the other leg is 12

Mar 31, 2017

Answer:

The second leg's length is #12#.

Explanation:

Math Warehouse

We'd use the pythagorean theorem to solve for the other leg's length. As the image suggests, we'd use the theorem, #a^2+b^2=c^2#.

If one leg is #9#, that's our #a# value.
If the hypotenuse is #15#, that's our #c# value.
Now we just have to find the #b# value.

Plugging in the variables, #9^2+b^2=15^2#.

#9^2=81#.
#15^2=225#.

#81+b^2=225#. Subtract #81# from both sides.

#b^2=144#. Square root both sides.

#sqrt(b^2)=b# and #sqrt(144)=12#, so #b=12#