As david approaches the counter at the department of motor vehicles, the clerk yells at david for having waited in the wrong line. david is convinced that the clerk should find another line of work-one in which his angry personality traits will not interfere with his job. however, david disregards the possibility that the department is short of that day. david has just fallen prey to the

Fundamental Attribution Error

This is the tendency for people to over-emphasize personality/attitude based explanations and under-emphasize situational/big picture explanations.

bd = 9 cm

step-by-step explanation:

in a 30°-60°-90° triangle, the ratio of side lengths is 1 : √3 : 2. that is, the longest side (hypotenuse) is twice the length of the shortest side.

all of the triangles in your geometry are 30°-60°-90° triangles. ac is the hypotenuse of δacd, and the short side of δabc.

the short side ad of δacd will be half the length of ac, so 3 cm. the hypotenuse ab of δabc will be twice the length of ac, so 12 cm. segment bd is the difference of the lengths ab and ad, so is

bd = ab -ad

bd = 12 cm - 3 cm = 9 cm

comment on side length ratios

you can figure the ratios of side lengths in a 30°-60°-90° triangle by considering the trig ratios of the angles. or you can figure the length of the altitude of an equilateral triangle of side length 2 using the pythagorean theorem.

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