Question

in triangleABC,AD|AC,AB=7.5cm,AC=100cm,AD=6cm.FindBC. so that angle BAC=90°​

Answer 1

Step-by-step explanation:

Given,

In \triangle ABC△ABC where AD\perp BC,AB=7.5\ cm,AC=10\ cm\ and\ AD=6\ cmAD⊥BC,AB=7.5 cm,AC=10 cm and AD=6 cm

From figure,

\angle ADB=\angle ADC=90\ degree∠ADB=∠ADC=90 degree

In \triangle ABD△ABD ,

AB^{2}=AD^{2}+BD^{2}AB

2

=AD

2

+BD

2

⇒AB^{2}-AD^{2}=BD^{2}AB

2

−AD

2

=BD

2

⇒(7.5)^{2}-6^{2}=BD^{2}(7.5)

2

−6

2

=BD

2

⇒BD=\sqrt{56.25-36}BD=

56.25−36

⇒BD=\sqrt{20.25}BD=

20.25

⇒BD=4.5\ cmBD=4.5 cm

In \triangle ACD△ACD ,

CD=\sqrt{AC^{2}-AD^{2} }CD=

AC

2

−AD

2

⇒CD=\sqrt{10^{2}-6^{2} }CD=

10

2

−6

2

⇒DC=8\ cmDC=8 cm

∴ BC=BD+CD=4.5+8=12.5\ cmBC=BD+CD=4.5+8=12.5 cm

From \triangle ABC△ABC ,

BC=\sqrt{AB^{2}+AC^{2} }BC=

AB

2

+AC

2

⇒BC=\sqrt{7.5^{2}+10^{2} }BC=

7.5

2

+10

2

⇒BC=12.5\ cmBC=12.5 cm

So, The value of BC=12.5\ cmBC=12.5 cm and \angle BAC=90\ degree∠BAC=90 degree in \triangle ABC△ABC .

Answer 2

Answer:

• ${\bf{\overline{BC}}} = 12.5 cm$ =

Step-by-step explanation:

In the figure, ABC is a right-angled triangle

Here,

➙ AD $\perp$ AC or, ∠ADC = 90°

➙ ∠BAC = 90°

‎ ‎ ‎ ‎→ AC = 100cm.

‎ ‎ ‎ ‎→ AD = 6cm.

‎ ‎ ‎ ‎→ BC = ?

To find ${\rm{\overline{BC}}}$ we'll use the ‘Pythagoras theorem’ in the triangle ABC

${\sf{\pink{\longrightarrow{h^2 = p^2 + b^2}}}}$

Where,

→ h = hypotenuse

→ b = base

→ p = perpendicular $\gray\perp$

We have,

→ BC (hypotenuse)

→ AB (base) = 7.5cm

→ AC (perpendicular) = 10cm.

We can say that,

⇒ BC² = AB² + AC²

⇒ BC² = 7.5² + 10²

⇒ BC² = 56.25 + 100

⇒ BC² = 156.25

⇒ BC = √156.25

⇒ BC = 12.5cm

$\therefore$ BC measures 12.5 cm.