Regents Geometry 5

Question 1

In a right triangle, sin(θ) = 5/13. What is cos(θ)?

Accepted Answer

12/13

Answer

cos(θ) = √(1 − (5/13)²) = √(144/169) = 12/13.

Question 2

What is the image of point (4, −3) after a 90° counterclockwise rotation about the origin?

Accepted Answer

(3, 4)

Answer

A 90° CCW rotation maps (x, y) → (−y, x), so (4, −3) → (3, 4).

Question 3

The volume of a cone is 150π cm³ and its height is 18 cm. What is its radius?

Accepted Answer

5 cm

Answer

V = (1/3)πr²h → 150π = (1/3)π r²(18) → r² = 25 → r = 5 cm.

Question 4

Two chords AB and CD intersect inside a circle at point P. If AP = 3, PB = 8, and CP = 4, what is PD?

Accepted Answer

6

Answer

Intersecting chords: AP × PB = CP × PD → 3 × 8 = 4 × PD → PD = 6.

Question 5

Which set of side lengths can form a triangle?

Accepted Answer

4, 5, 8

Answer

For {4, 5, 8}: 4+5=9 > 8, 4+8 > 5, and 5+8 > 4 — all triangle inequality conditions hold.

Regents Practice Test