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.

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