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The hypotenuse of a right triangle measures 16 cm and one of its legs measures 9 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.

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BrainlySamrat

[tex]\sf\huge\underline{\star Solution:-}[/tex]

Given that:

  • Hypotenuse of a right triangle = [tex]\sf\blue{16cm.}[/tex]
  • One side (leg) = [tex]\sf\blue{9cm.}[/tex]

To Find:

  • Measure of another side(leg).

Solution:-

[tex]\rightarrow[/tex] As we know that,

[tex]\sf{A^2 +B^2 \:=\: C^2}[/tex](Pythagoras Theorem)

So, using this formula we can find measure of another side(leg).

[tex]\rightarrow[/tex][tex]\sf{A^2 +B^2 \:=\: C^2}[/tex](putting the value of both given side of triangle)

  • Here I am putting the value of hypotenuse in C because it is the longest side of triangle.

[tex]\rightarrow[/tex] [tex]\sf{9^2 +B^2 \:=\: 16^2}[/tex]

[tex]\rightarrow[/tex] [tex]\sf{81 +B^2 \:=\: 256}[/tex]

[tex]\rightarrow[/tex] [tex]\sf{B^2 \:=\: 256-81}[/tex]

[tex]\rightarrow[/tex] [tex]\sf{B^2 \:=\: 175}[/tex]

[tex]\rightarrow[/tex] [tex]\sf{B \:=\: \sqrt{175}}[/tex]

[tex]\rightarrow[/tex] [tex]\sf{B\:=\: 13.22(approx)}[/tex]

Therefore, measure of another side (leg) of the triangle = [tex]\sf\purple{ 13.22(approx).}[/tex]

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Hope it helps you:)

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