Question

In AABC,<C=90° , 1(AC) = 5cm, 1(BC) = 12cm. What is the length of segment (AB)?
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Answer 1

Answer:

Triangle ABC with right angle from C is given in figure.

We know that angle bisector is a line that divides an angle into two half.

Here AC = 5 cm

BC = 12 cm (given)

\textbf{\Large Using Pythagorus Theorem :} a^2 + b^2 = c^2Using Pythagorus Theorem :a

2

+b

2

=c

2

So

\begin{gathered}5^2 + 12^2 = AB^2 \\\\25 + 144 = 169 = AB^2\\\end{gathered}

5

2

+12

2

=AB

2

25+144=169=AB

2

So AB = 13 cm

Now It is given that a bisector from A meets at D on the libe BC,

which makes angle DAC = 45°

So

By trigonometry

Cos 45° = \frac{\textbf{\large AC}}{\textbf{\large AD}} = \frac{ 1}{\sqrt 2}

AD

AC

=

2

1

As We know that AC = 5cm

\textbf{\large So the length of side AD}= 5\sqrt 2So the length of side AD=5

2

cm (Answer)