Chapter Exam

Unit 10: Properties of Triangles — Online MCQ Test

Q: In a triangle ABC, the sine rule states that a/sin A is equal to which of the following?

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.

Q: Which formula is used to find the cosine of an angle in a triangle when all three sides are known?

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.

Q: The projection rule in a triangle states that a = b·cos C + c·cos B. Which statement is NOT correct?

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.

Q: 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?

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.

MATHEMATICS - IA · CLASS 11 INTERMEDIATE 1 YEAR · Telangana State Board

Practice Unit 10: Properties of Triangles with a free chapter-wise online MCQ test for Telangana State Board CLASS 11 INTERMEDIATE 1 YEAR MATHEMATICS - IA. 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.... AI-generated questions from basic to board-exam level, with instant results and explanations.

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Unit 10: Properties of Triangles — Important Questions & Answers (FAQ)

Frequently asked questions from Telangana State Board CLASS 11 INTERMEDIATE 1 YEAR MATHEMATICS - IA — Unit 10: Properties of Triangles, with answers and explanations. These are sample questions; the exam has its own separate question set.

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.

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 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.

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.

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.