15-75-90 degree triangle. Find sides and area.

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Additional info on sines and cosines of 15 degrees:

30-60-90 degree triangle:

cos 15 - way to simplify nested square roots (square root inside of another square root):
  1. Sciency Sergei
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تمرين جميل جيد . رسم واضح مرتب . شرح واضح مرتب . شكرا جزيلا لكم . والله يحفظكم ويرعاكم ويحميكم جميعا . تحياتنا لكم من غزة فلسطين .

محمدنبي-دف
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You can find any trigonometric value without trigonometric expressions

Sin10 will be a nice one. Only geometry is enough. Thanks for your interesting videos

Mathematician
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There is a very interesting way. Reflect point A about BC, the new point be D. Now draw a circle circumscribing ABD, choose the circumcentre O, that is on BC. Join O, D and O, A

ODA is equilateral, so OA=OC=2x, and being the height OB=sqrt3 x, that immediately yields tan15=x /(2+sqrt3)x = 2-sqrt(3)

Edited : I didn't see you mentioned the same method in 8:30.

Mathematician