in a triangle ABC ,AD perpendicular to BC ,AB=7.5cm,AC=10 cm AD=6cm . show that angle BAC=90⁰
Answers
Answer:
The value of BC=12.5\ cmBC=12.5 cm and \angle BAC=90\ degree∠BAC=90 degree in \triangle ABC△ABC .
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 .
Step-by-step explanation:
hope you like it and markme brainleast