Regents Geometry 5 β Questions and Answers
Question 1: In a right triangle, sin(ΞΈ) = 5/13. What is cos(ΞΈ)?
- 12/13 (Correct answer)
- 5/12
- 13/12
- 13/5
Correct answer: 12/13
cos(ΞΈ) = β(1 β (5/13)Β²) = β(144/169) = 12/13.
Question 2: What is the image of point (4, β3) after a 90Β° counterclockwise rotation about the origin?
- (3, 4) (Correct answer)
- (β3, β4)
- (3, β4)
- (β4, β3)
Correct answer: (3, 4)
A 90Β° CCW rotation maps (x, y) β (βy, x), so (4, β3) β (3, 4).
Question 3: The volume of a cone is 150Ο cmΒ³ and its height is 18 cm. What is its radius?
- 3 cm
- 5 cm (Correct answer)
- 6 cm
- β150 cm
Correct answer: 5 cm
V = (1/3)ΟrΒ²h β 150Ο = (1/3)Ο rΒ²(18) β rΒ² = 25 β 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?
- 6 (Correct answer)
- 8
- 10
- 12
Correct answer: 6
Intersecting chords: AP Γ PB = CP Γ PD β 3 Γ 8 = 4 Γ PD β PD = 6.
Question 5: Which set of side lengths can form a triangle?
- 2, 3, 6
- 1, 5, 4
- 4, 5, 8 (Correct answer)
- 3, 3, 7
Correct answer: 4, 5, 8
For {4, 5, 8}: 4+5=9 > 8, 4+8 > 5, and 5+8 > 4 β all triangle inequality conditions hold.
Question 6: A dilation centered at the origin with scale factor 3 maps point (2, β1) to which point?
- (5, 2)
- (6, β3) (Correct answer)
- (β3, 6)
- (2/3, β1/3)
Correct answer: (6, β3)
Multiply each coordinate by 3: (2Γ3, β1Γ3) = (6, β3).
Question 7: A tangent and a secant are drawn from an external point. The tangent length is 6 and the external segment of the secant is 3. What is the whole length of the secant?
- 9
- 12 (Correct answer)
- 15
- 18
Correct answer: 12
TangentΒ² = external Γ whole: 36 = 3 Γ whole β whole = 12.
Regents Geometry 5
In a right triangle, sin(ΞΈ) = 5/13.
What is cos(ΞΈ)?