What is the length of the hypotenuse of a right triangle if the two other sides are of lengths 9 and 4?

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Answer 1 · 2018-04-02T04:23:36

Magnitude of the hypotenuse in the right triangle $\approx 9.85 u n i t s$ $~~"9.85 " units$

Given:

The right-triangle CAB, with $∠ C A B = 90^{\circ}$ $/_CAB=90^@$ .

$¯ ¯¯¯¯ ¯ A C = 4$ $bar (AC)=4$ units.

$¯ ¯¯¯¯ ¯ A B = 9$ $bar (AB) = 9$ units.

**Hypotenuse ** = $¯ ¯¯¯¯ ¯ B C$ $bar(BC)$

Pythagoras Theorem states that

${(B C)}^{2} = {(A C)}^{2} + {(A B)}^{2}$ $(BC)^2=(AC)^2+(AB)^2$

$\Rightarrow {(B C)}^{2} = 4^{2} + 9^{2}$ $rArr (BC)^2 = 4^2+9^2$

$\Rightarrow {(B C)}^{2} = 16 + 81$ $rArr (BC)^2 = 16+81$

$\Rightarrow {(B C)}^{2} = 97$ $rArr (BC)^2 = 97$

$\Rightarrow B C = \sqrt{97}$ $rArr BC = sqrt(97)$

$\Rightarrow B C \approx 9.848857802$ $rArr BC ~~ 9.848857802$

Hence,

magnitude of the hypotenuse in the right triangle $\approx 9.85 u n i t s$ $~~"9.85 " units$

Using a software, we can actually construct the right-triangle to scale, and prove our result as shown below:

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