find alpha angle in the triangle

Geometry Level 2


The answer is 40.

Aly Ahmed by Aly Ahmed , 34, Egypt

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3 solutions

Aly Ahmed
May 7, 2020

{: .cente||

1 Helpful 0 Interesting 0 Brilliant 0 Confused

nice approach!

nibedan mukherjee - 1 year, 1 month ago
Trupal Panchal
May 7, 2020

i tried very hard but won't able to find the method to solve for alpha then i actually draw it and measure the alpha which is 40.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

It's easy to get sin ⁡ α sin ⁡ 20 ° = sin ⁡ ( 70 ° + α ) sin ⁡ 30 ° ⟹ sin ⁡ α = 2 sin ⁡ 20 ° sin ⁡ ( 70 ° + α ) ⟹ cos ⁡ 40 ° sin ⁡ α = sin ⁡ 40 ° cos ⁡ α ⟹ tan ⁡ α = tan ⁡ 40 ° ⟹ α = 40 ° \dfrac {\sin α}{\sin 20\degree}=\dfrac {\sin (70\degree+α)}{\sin 30\degree}\implies \sin α=2\sin 20\degree\sin (70\degree+α)\implies \cos 40\degree\sin α=\sin 40\degree\cos α\implies \tan α=\tan 40\degree\implies α=\boxed {40\degree} .

0 Helpful 0 Interesting 0 Brilliant 1 Confused

your math is wrong dude, the third step should be 'cos(50) sin (alpha) = sin (50) cos (alpha)' because 70-20=50 not 40.

tell me if i miscalculated. thank you.

trupal panchal - 1 year, 1 month ago

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