Question

The altitude of a triangle ABC , in which A is an obtuse angle has length 10 cm if BD = 10 cm and CD = 10√3 cm . then, Determine angle A.

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Answer 1

Answer:

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Your question answer is => 105°

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Answer 2

Step-by-step explanation:

∆ ABC is a right triangle.

Given

AD = 10cm

BD = 10 cm

CD = 10√3 cm

Therefore,

Tan ∠BAD = BD/AD

tan∠BAD = 10/10 ⇒ 1

tan∠BAD = tan 45°

∠BAD = 45°. ... ( 1 )

∆ ACD is a right triangle.

Right angled at D, such that :-

AD = 10cm

CD = 10√3 cm

Therefore,

tan ∠CAD = CD/AD

tan ∠CAD = 10√3/10

⇒ √3

tan ∠CAD = tan 60°

∠CAD = 60° ... ( 2 )

FROM (1) AND (2) WE HAVE :-

∠BAC = ∠BAD + ∠CAD

⇒ 45° + 60°

⇒ 105°