Unit 10: Properties of Triangles — Online MCQ Test
MATHEMATICS - IA · CLASS 11 INTERMEDIATE 1 YEAR · Telangana State Board
Practice Unit 10: Properties of Triangles with a free chapter-wise online MCQ test.
This chapter covers: The final chapter examines relations between sides and angles of a triangle sine rule cosine rule projection rule tangent rule half-angle formulas inscribed excircle and circumcirc....
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Unit 10: Properties of Triangles — Important Questions & Answers
In a triangle ABC, the sine rule states that a/sin A is equal to which of the following?
- A. b/sin B = c/sin C = 2R
- B. b/sin C = c/sin B = R
- C. b·sin B = c·sin C = 2R
- D. sin B/b = sin C/c = 1/2R
Answer: A. b/sin B = c/sin C = 2R
The sine rule states that a/sin A = b/sin B = c/sin C = 2R, where R is the circumradius of the triangle.
The sine rule states that a/sin A = b/sin B = c/sin C = 2R, where R is the circumradius of the triangle.
Which formula is used to find the cosine of an angle in a triangle when all three sides are known?
- A. a = b + c - 2bc·cos A
- B. a² = b² + c² - 2bc·cos A
- C. cos A = (b² + c² - a²)/2bc
- D. sin A = (b² + c² - a²)/2bc
Answer: C. cos A = (b² + c² - a²)/2bc
The cosine rule rearranged gives cos A = (b² + c² - a²)/(2bc), allowing us to find the cosine of an angle when sides are known.
The cosine rule rearranged gives cos A = (b² + c² - a²)/(2bc), allowing us to find the cosine of an angle when sides are known.
The projection rule in a triangle states that a = b·cos C + c·cos B. Which statement is NOT correct?
- A. b = a·cos C + c·cos A
- B. c = a·cos B + b·cos A
- C. a = b·sin C + c·sin B
- D. All projections of two sides on the third equal that third side
Answer: C. a = b·sin C + c·sin B
The projection rule uses cosines, not sines. The projection of sides b and c on side a gives a = b·cos C + c·cos B, not sine values.
The projection rule uses cosines, not sines. The projection of sides b and c on side a gives a = b·cos C + c·cos B, not sine values.
In a triangle ABC with sides a, b, c and angles A, B, C respectively, which of the following correctly relates half-angles to sides?
- A. tan(A/2) = r/(s-a)
- B. tan(A/2) = (s-b)(s-c)/[s(s-a)]
- C. sin(A/2) = √[(s-b)(s-c)/(bc)]
- D. cos(A/2) = √[s(s-a)/(bc)]
Answer: D. cos(A/2) = √[s(s-a)/(bc)]
The half-angle formula is cos(A/2) = √[s(s-a)/(bc)], which relates the cosine of half an angle to the sides.
The half-angle formula is cos(A/2) = √[s(s-a)/(bc)], which relates the cosine of half an angle to the sides.
In a triangle, if two sides are a = 6, b = 8, and the included angle C = 90°, which statement is true about the circumradius?
- A. R equals 5 because the hypotenuse is the diameter
- B. R equals 7.5 calculated using the cosine rule
- C. R equals 10 from the sine rule with side c
- D. The triangle is right-angled with circumradius = c/2 = 5
Answer: D. The triangle is right-angled with circumradius = c/2 = 5
In a right triangle, the circumradius equals half the hypotenuse. Here c = √(36+64) = 10, so R = 5.
In a right triangle, the circumradius equals half the hypotenuse. Here c = √(36+64) = 10, so R = 5.