SAT Practice Questions: 30-60-90 Triangles - dummies

SAT Practice Questions: 30-60-90 Triangles

By Ron Woldoff

When you encounter a question on the SAT Math exam where you have to find the area of a triangle, you may end up treating it as a 30-60-90 triangle, even if it’s equilateral. (Fun fact: an equilateral triangle can be thought of as two 30-60-90 triangles!)

The following practice questions ask you to find the area of an equilateral triangle and then to find the area of a right triangle given only its hypotenuse and one of its angles.

Practice questions

  1. What is the area of an equilateral triangle with a base of 4?
    SAT1001_eq0801
  2. A certain right triangle has a hypotenuse of 2. If one of the angles is 30 degrees, what is the area of the triangle?
    SAT1001_eq0802

Answers and explanations

  1. The correct answer is Choice (A).
    You can find the area of an equilateral triangle by using the formula
    SAT1001_eq0803
    where s is any of the sides, including the base:
    SAT1001_eq0804
    You can also consider the equilateral triangle to be two 30-60-90 triangles, giving the triangle a height of
    SAT1001_eq0805
    then use the
    SAT1001_eq0806
  2. The correct answer is Choice (A).
    If one of the angles is 30 degrees, the other angle is 60 degrees, making this a 30-60-90 triangle, with a side ratio of
    SAT1001_eq0807
    The 2 is the hypotenuse, making the other two sides 1 and
    SAT1001_eq0808
    These numbers are also the base and height, so plug them into the formula for the area of a triangle:
    SAT1001_eq0809