Question

in right angled triangle ABC,if angleB=90°,AB=6,BC=8 then find AC​

Answer 1

Solution :-

By observing the given figure in the attachment

• The base of triangle is BC = 8
• The height of triangle is AB = 6

Here , we need to find AC in the figure

By the given information , the triangle has a right angle at B so it is a right angled triangle . And base & heigh are given , AC is hypotenuse . By this info finding AC using Pythagoras theorem .

Pythagoras theorem :- Square of Hypotenuse is equal to sum of square of base & square of height.

• In other form :-

→ Hypotenuse² = Base² + Height²

By substituting the values of hypotenuse , base & height ,

⇒ AC² = AB² + BC²

⇒ AC² = 6² + 8²

⇒ AC² = 36 + 64

⇒ AC² = 100

⇒ AC = √100

⇒ AC = 10 = Hypotenuse

Hence , the value of AC = 10

Answer 2

Answer:

✫ Given :-

• A right angle triangle ∆ABC where $\angle$B = 90°, AB = 6 cm and BC = 8 cm.

✫ To Find :-

• What is the value of AC.

Solution :-

➤ ∆ABC is a right angled triangle.

✯ By Pythagoras Theorem,

❖ $\boxed{\bold{\large{AC²\: =\: BC²\: AB²}}}$ ❖

$\implies$ AC² = 6² + 8²

$\implies$ AC² = 36 + 64

$\implies$ AC² = 100

$\implies$ AC = $\sqrt{100}$

➠ AC = 10 cm

$\therefore$ The value of AC is 10 cm.

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