What is the angle C?

Geometry Level 3

In a triangle △ A B C \triangle {ABC} , the median A D ‾ \overline {AD} is perpendicular to A B ‾ \overline {AB} . The measure of the ∠ B \angle B is 15 ° 15 \degree . What is the measure of the ∠ C \angle C in degrees?


The answer is 13.187.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

Dan Czinege
May 11, 2019

t g ( 15 ° + γ ) = 2 ∣ A D ∣ / ∣ A B ∣ tg(15°+γ)=2|AD|/|AB|
t g ( 15 ° + γ ) = 2 t g ( 15 ° ) tg(15°+γ)=2tg(15°)
( t g ( 15 ° ) + t g ( γ ) ) / ( 1 − t g ( 15 ° ) t g ( γ ) ) = 2 t g ( 15 ° ) (tg(15°)+tg(γ))/(1-tg(15°)tg(γ))=2tg(15°)
t g ( 15 ° ) + t g ( γ ) = 2 t g ( 15 ° ) − 2 t g 2 ( 15 ° ) t g ( γ ) tg(15°)+tg(γ)=2tg(15°)-2tg^2(15°)tg(γ)
t g ( γ ) = t g ( 15 ° ) / ( 1 + 2 t g ( 15 ° ) t g ( 15 ° ) tg(γ)=tg(15°)/(1+2tg(15°)tg(15°)
(tg(γ)=13,187° \ )


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