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konstantin123 [22]
2 years ago
8

Work out length of BC

Mathematics
2 answers:
weqwewe [10]2 years ago
8 0

\huge \tt \color{pink}{A}\color{blue}{n}\color{red}{s}\color{green}{w}\color{grey}{e}\color{purple}{r }

\large\underline{  \boxed{ \sf{✰\:Note }}}

★ 1st let's know what is the given figure is and it's related concepts for solving !

  • ➣ Given Triangle is a right angled triangle
  • ➣ It is having 3sides let's know what are the name of these sides
  • ➣ 1st AB is know as hypotenuse
  • ➣ 2nd AC and is called Base of the triangle
  • ➣ 3rd BC whích is know as perpendicular of the triangle
  • ➣ Hypotenuse(H):-The side of a right triangle opposite the right angle.
  • ➣ Perpendicular(P):- Exactly upright; extending in a straight line.
  • ➣ Base(B):- it also known as the side opposite to hypotenuse
  • ➣Perpendicular and base are know as the leg of right angled triangle
  • ➣ We can easily find length of one missing side by using a theorem name as "Pythagorean theorem"
  • ➣ Pythagorean theorem :- A mathematical theorem which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of those of the two other sides
  • ★ Note :- The Pythagorean theorem only applies to right triangles.

\rule{70mm}{2.9pt}

★ Writing this theorem mathematically ★

{ \boxed{✫\underline{  \boxed{ \sf{Pythagorean \:  theorem  \: ⇒ {Hypotenuse }^2={ Base }^2+ {Height }^2}}}✫}}

★ Here ★

  • ➣ Base (AC)= 8cm
  • ➣ Hypotenuse (BA)= 13cm

\rule{70mm}{2.9pt}

<h3>✝ Assumption ✝</h3>
  • ➣ let perpendicular/length ( BC ) = "x"
<h3 />

\boxed{ \rm{ \pink ➛BA^2= AC^2+BC^2}}

\rule{70mm}{2.9pt}

<h3>✝ let's substitute values ✝</h3>

\rm{ \pink ➛13^2= 8^2+x^2} \\ \rm{ \pink ➛169 = 64 +  {x}^{2} } \\ \rm{ \pink ➛169 - 64  =  {x}^{2} } \\ \rm{ \pink ➛105 =  {x}^{2}}  \\ \rm{ \pink ➛ \sqrt{105} \: or \: 10.2469  = x} \\

\rule{70mm}{2.9pt}

Hence length (BC) in the given triangle is of

{ \boxed{✛\underline{  \boxed{ \sf{\sqrt{105} cm\: or \: 10.2469cm\green✓}}}✛}}

\rule{70mm}{2.9pt}

Hope it helps !

Neporo4naja [7]2 years ago
3 0

Answer:

assume 13 = z \\ 8 =x  \\ bc = y

by phytagorean theorem

{y}^{2}  +  {x}^{2}  = z^{2}

so

bc = y =  \sqrt{ {z}^{2}  -  {x}^{2} } =  \sqrt{169 - 64}   =  \sqrt{105}

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