Triangle ABC is a right triangle. If side #AC=7# and side #BC=10#, what is the measure of side AB?

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Answer 1 · 2018-05-15T12:09:52

It's not clear which one's the hypotenuse so either #\sqrt{7^2+10^2}=sqrt{149}# or #sqrt{10^2-7^2}=sqrt{51}#.

Answer 2 · 2018-05-15T12:10:14

It depends on who is the hypothenuse

If #AC# and #BC# are both legs, then #AB# is the hypothenuse, and you have

#\overline{AB}^2 = \overline{BC}^2+\overline{AC}^2#

from which you deduce

#\overline{AB} = sqrt(\overline{BC}^2+\overline{AC}^2) = sqrt(100+49) = sqrt(149)#

If, instead, #BC# is the hypoyhenuse, you have

#\overline{AB} = sqrt(\overline{BC}^2-\overline{AC}^2) = sqrt(100-49) = sqrt(51)#

Answer 3 · 2018-05-15T12:11:29

Depending on which is the right angle, either #sqrt(51)# or #sqrt(149)#

Using Pythagoras, (#hypoten use^2=Arm^2+Arm^2#)

If BC is the hypotenuse,
#100=49+AB^2#
#AB=sqrt(51)# (length must be positive)

However, if AB is the hypotenuse, then
#AB^2=100+49#
#AB=sqrt(149)# (length must be positive)

AC cannot be the hypotenuse as it is shorter than BC.