Sat math Essentials

16.
e.
FDCB
is a rectangle, which means that angle 
D
is a right angle. Angle 
ECD
is 60 degrees, which
makes triangle 
EDC
a 30-60-90 right triangle.
The leg opposite the 60-degree angle is equal to
3
times the length of the leg opposite the 
30-degree angle. Therefore, the length of side
DC
is equal to 
6
3
, or 2
3
. The hypotenuse of a
30-60-90 right triangle is equal to twice the
length of the leg opposite the 30-degree angle, so
the length of
EC
is 2(2
3
) = 4
3
. Angle 
DCB
is also a right angle, and triangle 
ABC
is also a
2
h
2
h
g
–
P R A C T I C E T E S T 2
–
2 1 9

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30-60-60 right triangle. Since angle 
ECD
is 60
degrees, angle 
ECB
is equal to 90 – 60 = 30
degrees. Therefore, the length of
AC
, the
hypotenuse of triangle 
ABC
, is twice the length
of
AB
: 2(10) = 20. The length of
AC
is 20 and the
length of
EC
is 4
3
. Therefore, the length of
AE
is 20 – 4
3
.
–
P R A C T I C E T E S T 2
–
2 2 0

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W
hen you are finished, review the answers and explanations that immediately follow the test.
Make note of the kinds of errors you made and review the appropriate skills and concepts before
taking another practice test.
C H A P T E R
Practice Test 3
This practice test is a simulation of the three Math sections you will
complete on the SAT. To receive the most benefit from this practice test,
complete it as if it were the real SAT. So take this practice test under
test-like conditions: Isolate yourself somewhere you will not be dis-
turbed; use a stopwatch; follow the directions; and give yourself only
the amount of time allotted for each section.