Question

.. In a right-angled triangle ABC, angleB = 90°
(1) If AB = 8 cm, BC = 15 cm, find AC.
(ii) If AC = 26 cm, AB = 24 cm, find BC.​

Answer 1

Answer:

See the attachment. It will surely help you...

Step-by-step explanation:

Answer 2

Concept:

Here, we have to use Concept of Pythagoras Theorem. We are given a right angled triangle, we have to find the length of sides if length of two sides are given. We are given with two conditions. So, Using Pythagoras theorem in each condition we will get the length of the sides.

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Given: In Right angled triangle ABC, ∠B equals to 90°.

To Find: ❍ If AB equals to 8cm and BC equals to 15cm. Find AC . ❍ If AC equals to 26cm and AB equals to 24cm. Find BC

Formula to be Used:$\sf{{Perpendicular}^{2}+{Base}^{2}={Hypotenuse}^{2}}$

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Solution:

⟩ If AB equals to 8cm and BC equals to 15cm We have to find the length of AC.

So, According to the given condition-

› AB = 8cm

› BC = 15cm

Using Pythagoras theorem-

$\mapsto\sf{{AC}^{2}={AB}^{2}+{BC}^{2}}$

$\mapsto\sf{{AC}^{2}={8}^{2}+{15}^{2}}$

$\mapsto\sf{{AC}^{2}=64+225}$

$\mapsto\sf{{AC}^{2}=289}$

$\mapsto\sf{AC=\sqrt{289}}$

$\mapsto\bold{AC=17}$

$\: \: \: \: \: \: \therefore\sf{\underline{\color{purple}{Hence\: Length\: of\: AC\: is\: 17\: cm}}}$

⟩ If AC equals to 26cm and AB equals to 24cm. We have to find the length of BC.

So, According to the given condition-

› AC = 26cm

› AB = 24cm

Using Pythagoras theorem-

$\rightarrow\sf{{AC}^{2}={AB}^{2}+{BC}^{2}}$

$\rightarrow\sf{{26}^{2}={24}^{2}+{BC}^{2}}$

$\rightarrow\sf{676=576+{BC}^{2}}$

$\rightarrow\sf{676-576={BC}^{2}}$

$\rightarrow\sf{{BC}^{2}=100}$

$\rightarrow\sf{BC=\sqrt{100}}$

$\rightarrow\bold{BC=10}$

$\: \: \: \: \: \: \therefore\sf{\underline{\color{purple}{Hence\: Length\: of\: BC\: is\: 10\: cm}}}$