Question

The altitudeAD of a triangle ABC in which CA obtuse and AD is equal to 10 cm if BD is equal 10 cm and CD is equal to 10 root 3 cm determine angle A​

Answer 1

Answer:

angle A is105degree

Step-by-step explanation:

The altitude AD of ΔABC in which ∠A obtuse and AD = 10 cm. If BD = 10 cm and CD = 10

3

cm, determine ∠A.

November 22, 2019avatar

Afroze Raichand

SHARE

ANSWER

ΔABC is a right triangle , right angled at D such that = 10 cm and BD = 10 cm

∴tan∠BAD=

AD

BD

⇒tan∠BAD=

10

10

=1

⇒tan∠BAD=tan45

∘

TRIGONOMETRICRATIOS

⇒∠BAD=45

∘

ΔACD is a right triangle right angled at D such that AD = 10 cm and DC = 10

3

cm.

∴tan∠CAD=

AD

CD

⇒tan∠CAD=

10

10

3

=

3

⇒tan∠CAD=tan60

∘

∴∠CAD=60

∘

From (i) and (ii) , we have

∠BAC=∠BAD+∠CAD=45

∘

+60

∘

=105