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SAT Math: Geometry and Trigonometry (Drill 2)

Drill 2 · Math · Geometry and Trigonometry

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About This Drill

SAT Math: Geometry and Trigonometry (Drill 2) is a Math practice drill covering Geometry and Trigonometry. It contains 5 original questions developed by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

SAT geometry and trigonometry questions test special right triangles (30-60-90 and 45-45-90), volume of solids, cofunction identities, surface area, and similarity ratios. This drill requires applying geometric properties to solve multi-step measurement problems.

Questions & Explanations

Question 1. In a 30-60-90 triangle, the hypotenuse has length 10. What is the length of the side opposite the 60° angle?

  • A) 5
  • B) 5√3 ✓
  • C) 10√3
  • D) 10

Explanation: Sides are x : x√3 : 2x. Hypotenuse = 2x = 10, so x = 5. Side opposite 60° = 5√3.

Question 2. A cone has a radius of 6 and a height of 9. What is the volume of the cone?

  • A) 54π
  • B) 162π
  • C) 108π ✓
  • D) 324π

Explanation: V = (1/3)πr²h = (1/3)π(36)(9) = 108π. Choice D is πr²h without the 1/3 factor.

Question 3. If sin 35° = 0.574, what is the value of cos 55°?

  • A) 0.574 ✓
  • B) 0.819
  • C) 0.426
  • D) 0.342

Explanation: Cofunction identity: sin(θ) = cos(90° − θ). Since 35° + 55° = 90°, sin 35° = cos 55° = 0.574.

Question 4. A rectangular box has length 8, width 5, and height 3. What is the total surface area?

  • A) 79
  • B) 120
  • C) 128
  • D) 158 ✓

Explanation: SA = 2(lw + lh + wh) = 2(40 + 24 + 15) = 2(79) = 158. Choice A forgets to multiply by 2.

Question 5. Two similar triangles have corresponding sides in proportion. The smaller has sides 6, 8, 10. If the medium side of the larger is 12, what is the shortest side of the larger?

  • A) 7.5
  • B) 9 ✓
  • C) 10
  • D) 12

Explanation: Scale factor = 12/8 = 1.5. Shortest side = 6 × 1.5 = 9.