Geometric glamour
Geometry
Level
2
Find the length of side AB in the figure below. Round your answer to 3 significant digits.
The answer is 7.17.
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1 solution
Note that triangle DAC is isosceles and therefore if we draw the perpendicular from D to AC, it will cut AC into two halves and bisect angle D. Hence
(1/2) AC = 10 sin(35) or AC = 20 sin(35)
Note that the two internal angles B and C of triangle ABC add up to 90 and therefore the third angle of triangle ABC is a right angle. We can therefore write
tan(32) = AB / AC
Which gives AB = AC tan(32)
= 20 sin(35)tan(32) = 7.17 ( rounded to 3 significant digits)