In the figure above, ΔABC is similar to ΔXYZ. What is the value of cos A?A)B)
C)
D) 2
Here’s How to Crack It
Because the two triangles are similar, the value of corresponding trigonometric functions will be equal.
Therefore, cos A = cos X. The value of cos X is or . You could use the Pythagorean
Theorem to find XY, but it’s easier to use the special right triangle discussed earlier. Because the
hypotenuse is twice one of the legs, you know this is a 30°-60°-90° triangle. YZ is the shortest side (x), so
XY is x or 2 . Therefore, cosX = , which reduces to . Because cos X = cos A, cos A also
equals , which is (B).
Circles
Here are the rules you’ll need to tackle circle questions on the SAT.
- The circumference of a circle is 2πr or πd, where r is the radius of the circle and d is the
diameter.