SAT Practice Math Questions: Trigonometry Using SOH CAH TOA

By Geraldine Woods, Ron Woldoff

Most SAT trigonometry questions are based on trigonometric ratios, which are the relationships between the angles and sides of a right triangle in terms of one of its acute (less than 90 degrees) angles.

You can answer almost every SAT trig question by using the mnemonic device for the three basic trigonometric ratios: SOH CAH TOA.

SOH CAH TOA stands for

2001

Try some examples.

Practice questions

  1. For the right triangle,

    2002

    what is the sine of angle A?

    2003

  2. For the right triangle,

    2004

    if tan B =

    2005

    find cos A.

    2006

Answers and explanations

  1. D. Using the SOH in SOH CAH TOA, you know that the sine of angle A comes from the opposite (1) over the hypotenuse (2), for an answer of 1/2.
  2. D. If tan B =

    2007

    and tangent is opposite over adjacent (the TOA from SOH CAH TOA), then draw the triangle like this:

    2008

    Spotting this as one of the Pythagorean triples, you automatically throw the 5 down onto the hypotenuse:

    2009

    Cosine is CAH, which is adjacent over hypotenuse. Therefore, cos A =

    2010