Cracking The SAT Premium

the volume  is  16,500, the depth   (or height) is  10, and the length  is  75. Just    put those   numbers in

the formula:    16,500  =   75  ×   w   ×   10. Use your    calculator  to  solve   for w,  which   equals  22: Choice

(A) is  correct.

8. C The    5   equal   lengths that    make    up  the two sides   of  the largest triangle    tell    us  that    we  are dealing

with    5   similar triangles.  The largest triangle    has sides   15:25:30,   and the sides   of  all 5   triangles

will    have    an  equivalent  ratio.  Reduced,    the ratio   is  3:5:6,  which   happens to  be  the dimensions

of  the smallest    triangle.   We  want    to  find    the length  of  BD, the base    of  a   triangle    with    sides   of  6

and 10. This    is  twice   as  big as  the smallest    triangle,   so  the base    BD  must    be  6   ×   2   =   12, which

is  (C).

12. C Use SOHCAHTOA and your calculator to find the height of the flagpole. From the 70° angle,

you know    the adjacent    side    of  the triangle,   and you want    to  find    the opposite    side,   so  you need

to  use tangent.    Tangent =    ,  so  tan 70° =    ,  where   x   is  the height  of  the flagpole    up  to

the ball.   Isolate x   by  multiplying both    sides   by  10: 10  tan 70° =   x.  Use your    calculator  to  find

that    10  tan 70° =   27.47,  which   is  closest to  (C).

26. 
    

    D Don’t forget that you can plug in numbers on geometry questions. Let’s make b = 70° and a =
    30°. So the third angle in the triangle is 80°. You know that c would be 80°, because it is
    opposite an 80° angle. Your target answer is a = 30°, so plug in 80° and 70° to find it. The only
    possible answer is (D).

    
    


27. 
    

    B There’s a lot going on in this problem! But if we take it piece by piece, we’ll crack it. Let’s
    start filling in some information. The first thing the problem tells us is that triangle ABC is
    equilateral. Mark 60 degree angles on the figure. Next, we see that angle AEF is a right angle.
    Write that in as well. The problem also conveniently tells us that D and F are the midpoints of
    AB and AC, respectively. Therefore, AD and AF are 2. Finally, the last piece of information
    reveals that E is the midpoint of DF; mark DE and EF as equal.

    
    

Now,    what    do  we  have?   Triangle    AEF is  a   right   triangle,   with    a   hypotenuse  of  2   and a   leg of  1.

Hmm,     perhaps     the     good    ol’     Pythagorean     Theorem     can     help    us.     Plug    the     numbers     into    the

formula,    and you’ll  find    that    the answer  is  (B).

You  may     have    also    noticed     that    triangle   ADE  is  a   30°-60°-90°     triangle    with    hypotenuse  2,

which   means   that    DE  is  1   and w,  opposite    the 60°,    is  the square  root    of  3.  In  geometry    questions

on  the SAT,    there   will    often   be  multiple    ways    to  get to  the answer. On  the day of  the test,   use

whichever   method  you are most    comfortable with.

29. B Work the problem in steps. You are given the mass, so to find density you need to find the

volume  of  the pyramid.    The formula at  the beginning   of  the section tells   you that,   for a   pyramid,