How do you find the missing side of a right triangle given a = 5, b = 10?

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How do you find the missing side of a right triangle given a = 5, b = 10?

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Answer 1 · 2016-04-10T13:59:22

Use of Pythagora'sTheorem

Explanation:

$h y p^{2}$ $hyp^2$ = $o p p^{2}$ $opp^2$ + $a d j^{2}$ $adj^2$
Replace values....

$10^{2}$ $10^2$ = $5^{2}$ $5^2$ + $s i d e^{2}$ $side^2$
100= 25 + $s i d e^{2}$ $side^2$
100-25= $s i d e^{2}$ $side^2$
75= $s i d e^{2}$ $side^2$
side= $\sqrt{75}$ $sqrt75$

Answer 2 · 2016-04-10T14:14:40

$5 \sqrt{5}$ $5sqrt5$

Explanation:

Note: I am considering $a and b$ $aandb$ are the right containing sides

Consider the diagram

enter image source here

Use Pythagoras theorem

$a^{2} + b^{2} = c^{2}$ $color(blue)(a^2+b^2=c^2$

Where,

$a and b$ $aand b$ are the right-containing sides, and $c$ $c$ is the Hypotenuse

(Hypotenuse is the longest side of a right triangle)

$\to 5^{2} + 10^{2} = c^{2}$ $rarr5^2+10^2=c^2$

$\to 25 + 100 = c^{2}$ $rarr25+100=c^2$

$\to 125 = c^{2}$ $rarr125=c^2$

Take the square root of both sides

$\to \sqrt{125} = {\sqrt{c}}^{2}$ $rarrsqrt125=sqrtc^2$

$\Rightarrow c = \sqrt{125} = \sqrt{5 \cdot 5 \cdot 5} = 5 \sqrt{5}$ $color(green)(rArrc=sqrt125=sqrt(5*5*5)=5sqrt5$

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How do you find the missing side of a right triangle given a = 5, b = 10?

2 Answers

Explanation:

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