Question

In right angled triangle ABC, ∆A = 90°, BC = 10 cm,
AB = 6 cm, then find AC.​

Answer 1

Answer:

The measure of AC in ∆ABC is 8 cm .

Step-by-step explanation:

In ∆ ABC :

• ∠A = 90°
• BC = 10 cm
• AB = 6 cm
• AC = ??

As the given triangle is a right angled triangle, we'll be using PYTHAGORAS THEOREM.

According to Pythagoras theorem:

• Hypotenuse = BC = 10 cm
• Base = AC = x
• Height = BA = 6 cm

★ (Hypotenuse)² = (Base)² + (Height)²

⇒ (10)² = x² + 6²

⇒ 100 = x² + 36

⇒ x² = 100 - 36

⇒ x² = 64

⇒ x = √64

⇒ x = 8

Base = 8 cm

So, AC = 8 cm

Therefore, the measure of AC in ∆ABC is 8 cm.

Answer 2

Answer:

• 8 cm.

Step-by-step explanation:

Given

• In a right angled triangle ABC

1. ∠A = 90°
2. BC = 10 cm
3. AB = 6 cm

To find

• AC = ? cm

Solution

➝ In Δ ABC :

• ∠A = 90°

➝ (Hypotenuse)² = (Base)² + (Height)²

Here :

• (BC)² = (AC)² + (AB)²

Substituting we get :

• (10)² = (AC)² + (6)²
• 100 = (AC)² + 36
• (AC)² = 100 - 36
• (AC)² = 64
• AC = √64
• AC = 8 cm

Hence, the measure of AC is 8 cm.

Verification

• (Hypotenuse)² = (Base)² + (Height)²
• (10)² = (8)² + (6)²
• 100 = 64 + 36
• 100 = 100
• L.H.S = R.H.S