SAT Math: Geometry and Trigonometry (Drill 3)

Question 1. In a right triangle, one leg is 5 and the hypotenuse is 13. What is the length of the other leg?

• A) 8
• B) 10
• C) 12 ✓
• D) 11

Explanation: By the Pythagorean theorem: a² + 5² = 13². a² = 169 − 25 = 144. a = 12.

Question 2. A cylinder has radius 4 and height 10. What is its volume?

• A) 40π
• B) 80π
• C) 160π ✓
• D) 640π

Explanation: V = πr²h = π(16)(10) = 160π.

Question 3. In a 45-45-90 triangle, the hypotenuse is 10. What is the length of each leg?

• A) 5
• B) 5√2 ✓
• C) 10√2
• D) 5√3

Explanation: In a 45-45-90 triangle, hypotenuse = leg × √2. So leg = 10/√2 = 10√2/2 = 5√2.

Question 4. In right triangle ABC, angle C = 90° and sin(A) = 5/13. What is cos(A)?

• A) 5/13
• B) 12/13 ✓
• C) 5/12
• D) 13/12

Explanation: sin(A) = 5/13 means opposite = 5, hypotenuse = 13. Adjacent = √169 − 25 = 12. cos(A) = 12/13.

Question 5. Two similar triangles have a scale factor of 3:5. If the area of the smaller triangle is 27 cm², what is the area of the larger triangle?

• A) 45 cm²
• B) 75 cm² ✓
• C) 135 cm²
• D) 225 cm²

Explanation: Area scales as the square of the linear scale factor: (3/5)² = 9/25. So 27/x = 9/25. x = 27 × 25/9 = 75 cm².