Question

Find the length of side AC in the right triangle ABC with sides AC = 13 cm, BC = 5 cm and <B = 90 degree.Required to answer. Single choice. l will mark you brainliest​

Answer 1

Correct Question

Find the length of side AB in the right triangle ABC with sides AC = 13 cm, BC = 5 cm and ∠B = 90 degree.

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Given

• AC = 13 cm
• BC = 5 cm
• ∠B = 90°

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To Find

• Length of AB

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Solution

We know that the given triangle is a right angled triangle since one of the angles is equal to 90°.

To find the value of AB, we will apply Pythagorean Theorem.

Pythagorean Theorem ⇒ (Base)² + (Height)² = (Hypotenuse)²

Let's assume,

• AB to be the Height
• BC to be the Base
• AC to be the Hypotenuse

⇒ (AB)² + (BC)² = (AC)²

⇒ (AB)² + (5)² = (13)²

⇒ (AB)² + 25 = 169

⇒ (AB)² = 169 - 25

⇒ (AB)² = 144

⇒ AB = √144

⇒ AB = 12

∴ The value of AB would be 12 cm.

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Answer 2

Question –

Find the length of side AB in the right triangle ABC with sides AC = 13 cm, BC = 5 cm and < B = 90 degree.

Answer –

Given that -

• A triangle ABC is given.

• AC measures = 13 cm.

• BC measures = 5 cm.

• Angle B measures = 90°.

To find -

• Measure of AB.

Solution -

• Measure of AB = 12 cm

Using concept -

• Phythagoras theorm.

Using formula -

• Phythagoras theorm = (Base)² + (Height)² = (Hypotenuse)²

Assumptions -

• Let AB as the Height.

• Let BC as the Base.

• Let AC as the Hypotenuse.

We also write these as -

• Height as H.

• Base as B

• Hypotenuse as H.

• Angle as <

• Triangle as ∆

• Perpendicular as P.

What does the question say ?

Let's understand concept 1st !

• This question says that there is a triangle given named ABC. The length of AC is given as 13 cm. The length of BC = 5 cm. Afterwards it ask us to find the measure of AB. And it is also given that Angle B measures 90 degree. And by seeing this we have cleared that the traingle is a right-angled triangle because it's one angle measure 90°

How to do this question ?

Let's see procedure now !

• To solve this question we have to use phythagoras theorm and it's formula is Phythagoras theorm = (Base)² + (Height)² = (Hypotenuse)². Now according to this formula we have to put the values afterthat we get our final result that is

Full solution -

Using phythagoras theorm's formula

➝ Phythagoras theorm = (Base)² + (Height)² = (Hypotenuse)².

Here,

• Base as BC.

• Height as AB 5

• Hypotenuse as AC 13

➝ Phythagoras theorm = (Base)² + (Height)² = (Hypotenuse)².

➝ Phythagoras theorm = (BC)² + (AB)² = (AC)²

Where,

• AB is 5 cm.

• AC is 13 cm

➝ Phythagoras theorm = (BC)² + (5)² = (13)²

➝ Phythagoras theorm = (BC)² + 25 = 169

➝ Phythagoras theorm = (BC)² = 169 - 25

➝ Phythagoras theorm = (BC)² = 144

➝ Phythagoras theorm = BC = √144

➝ Phythagoras theorm = BC = 12 cm

Hence, 12 cm is the answer.

Since, the measure of AB is 12 cm.

More knowledge –

Pythagoras theorem = It state that in a right-angled triangle, the ² of the h side = the sum of squares of the other two sides. The sides of this ∆ have been named as Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°.

Formula to find Pythagoras theorem = (Base)² + (Height)² = (Hypotenuse)².

Diagram of triangle ( Phythagoras theorm ) = Above attachment.