CHAPTER DRILL ANSWERS AND EXPLANATIONS
Geometry Drill 1: No Calculator Section
2. B Because the question wants arc length and gives you the measure of the central angle in radians,
you can use the formula s = rθ to find the arc length: s = (8) = π, which reduces to
π, which is (B).
3. C Tangent is defined as . The side opposite angle XZY is 7, and the side adjacent to this
angle is 8, so the tangent of XZY = , which is (C).
10. A You can plug in when you’re dealing with a geometry problem with unknowns. When you’re
Plugging In for a right triangle, use one of the special right triangles to make your life easier.
Use a 3-4-5 right triangle. Make the side opposite a 3, the side adjacent to a 4, and the
hypotenuse 5. Because sine is , sin a = , so x = . Cosine is , so cos b
= . This is your target; circle it. Make x = in each answer choice and look for the answer
which equals . Only (A) works.
15. C The trick is to recognize that ∆ABC is a 30°-60°-90° right triangle. ABC must equal 90° since
a tangent line must be perpendicular to the radius of a circle drawn to the point of tangency.
Only a 30°-60°-90° has a hypotenuse (AC) equal to double the length of one of the sides (AB).
(You can also use the Pythagorean Theorem to show this.) This means that BAC = 60°, so the
shaded region has a central angle measure of 360° – 60° = 300°. To get the area, use the
proportion . Reduce, cross-multiply, and solve to
get s = 17.5. This matches (C).
Geometry Drill 2: Calculator-Permitted Section
1. A For this question, you need to know that volume equals length × width × height. You know that
