Kyle and alyssa paid $1,000 and $4,000 in qualifying expenses for their two daughters jane and jill, respectively, to attend the university of california. jane is a sophomore and jill is a freshman. kyle and alyssa's agi is $135,000 and they file a joint return. what is their allowable american opportunity tax credit after the credit phase-out based on agi is taken into account?
bd = 9 cm
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.