Q. In triangle ABC, if AB = 10 cm, AC = 6 cm, and angle A = 30°, what is the length of side BC?
A.
8 cm
B.
7 cm
C.
5 cm
D.
4 cm
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Solution
Using the Law of Cosines: BC² = AB² + AC² - 2 * AB * AC * cos(A) = 10² + 6² - 2 * 10 * 6 * (√3/2) = 100 + 36 - 60√3. BC = √(100 + 36 - 60√3) ≈ 7 cm.
Correct Answer: B — 7 cm
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Q. In triangle ABC, if AB = 7 cm, AC = 24 cm, and BC = 25 cm, is triangle ABC a right triangle?
A.
Yes
B.
No
C.
Cannot be determined
D.
Only if angle A is 90°
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Solution
Using the Pythagorean theorem, 7^2 + 24^2 = 49 + 576 = 625 = 25^2, so triangle ABC is a right triangle.
Correct Answer: A — Yes
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Q. In triangle ABC, if AB = 7 cm, AC = 24 cm, and BC = 25 cm, what is the area of the triangle?
A.
84 cm²
B.
96 cm²
C.
120 cm²
D.
140 cm²
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Solution
Using Heron's formula, the semi-perimeter s = (7 + 24 + 25)/2 = 28. Area = √[s(s-a)(s-b)(s-c)] = √[28(28-7)(28-24)(28-25)] = √[28*21*4*3] = 84 cm².
Correct Answer: B — 96 cm²
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Q. In triangle ABC, if AB = 8, AC = 6, and BC = 10, what is the semi-perimeter?
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Solution
Semi-perimeter s = (AB + AC + BC) / 2 = (8 + 6 + 10) / 2 = 12.
Correct Answer: B — 14
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Q. In triangle ABC, if angle A = 45 degrees and angle B = 45 degrees, what is angle C?
A.
45 degrees
B.
60 degrees
C.
90 degrees
D.
135 degrees
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Solution
The sum of angles in a triangle is 180 degrees. Therefore, angle C = 180 - (45 + 45) = 90 degrees.
Correct Answer: C — 90 degrees
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Q. In triangle ABC, if angle A = 45 degrees and angle B = 45 degrees, what is the relationship between sides a, b, and c?
A.
a = b
B.
a > b
C.
a < b
D.
a + b = c
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Solution
In an isosceles triangle with angles A and B equal, the sides opposite those angles are equal, hence a = b.
Correct Answer: A — a = b
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Q. In triangle ABC, if angle A = 45 degrees and angle B = 45 degrees, what is the type of triangle?
A.
Scalene
B.
Isosceles
C.
Equilateral
D.
Right
Show solution
Solution
Since two angles are equal, triangle ABC is isosceles.
Correct Answer: B — Isosceles
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Q. In triangle ABC, if angle A = 45 degrees and side a = 10 cm, what is the length of side b if angle B = 60 degrees?
A.
8.66 cm
B.
10 cm
C.
12.25 cm
D.
15 cm
Show solution
Solution
Using the Law of Sines: a/sin(A) = b/sin(B). Therefore, b = a * (sin(B)/sin(A)) = 10 * (sin(60)/sin(45)) = 10 * (√3/2)/(√2/2) = 10 * √3/√2 = 10 * √(3/2) = 8.66 cm.
Correct Answer: A — 8.66 cm
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Q. In triangle ABC, if angle A = 45° and angle B = 45°, what is angle C?
A.
45°
B.
60°
C.
75°
D.
90°
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Solution
Angle C = 180° - (angle A + angle B) = 180° - (45° + 45°) = 90°.
Correct Answer: D — 90°
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Q. In triangle ABC, if angle A = 45° and side a = 10, what is the length of side b if angle B = 60°?
A.
8.66
B.
7.5
C.
5
D.
10
Show solution
Solution
Using the Law of Sines: b/a = sin(B)/sin(A) => b = a * (sin(B)/sin(A)) = 10 * (√3/2)/(√2/2) = 10 * √3/√2 = 10 * 8.66/10 = 8.66.
Correct Answer: A — 8.66
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Q. In triangle ABC, if angle A = 60 degrees and angle B = 70 degrees, what is angle C?
A.
50 degrees
B.
60 degrees
C.
70 degrees
D.
80 degrees
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Solution
Angle C = 180 - (angle A + angle B) = 180 - (60 + 70) = 50 degrees.
Correct Answer: A — 50 degrees
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Q. In triangle ABC, if angle A = 60 degrees and angle B = 70 degrees, what is the measure of angle C?
A.
50 degrees
B.
60 degrees
C.
70 degrees
D.
80 degrees
Show solution
Solution
The sum of angles in a triangle is 180 degrees. Therefore, angle C = 180 - (60 + 70) = 50 degrees.
Correct Answer: A — 50 degrees
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Q. In triangle ABC, if angle A = 60° and angle B = 70°, what is angle C?
A.
50°
B.
60°
C.
70°
D.
80°
Show solution
Solution
Angle C = 180° - (angle A + angle B) = 180° - (60° + 70°) = 50°.
Correct Answer: A — 50°
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Q. In triangle ABC, if the angles are in the ratio 2:3:4, what is the measure of the largest angle?
A.
60 degrees
B.
80 degrees
C.
90 degrees
D.
120 degrees
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Solution
Let the angles be 2x, 3x, and 4x. Then, 2x + 3x + 4x = 180 => 9x = 180 => x = 20. The largest angle = 4x = 80 degrees.
Correct Answer: B — 80 degrees
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Q. In triangle ABC, if the coordinates of A, B, and C are (1, 2), (4, 6), and (7, 2) respectively, what is the area of triangle ABC?
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Solution
Using the formula for the area of a triangle given vertices, Area = 1/2 | x1(y2-y3) + x2(y3-y1) + x3(y1-y2) | = 1/2 | 1(6-2) + 4(2-2) + 7(2-6) | = 1/2 | 4 + 0 - 28 | = 12.
Correct Answer: A — 12
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Q. In triangle ABC, if the coordinates of A, B, and C are (1, 2), (4, 6), and (7, 2) respectively, what is the length of side AB?
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Solution
Length of AB = √[(4-1)² + (6-2)²] = √[3² + 4²] = √[9 + 16] = √25 = 5.
Correct Answer: B — 5
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Q. In triangle ABC, if the lengths of sides a = 10, b = 24, and angle C = 60 degrees, find the length of side c.
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Solution
Using the cosine rule: c^2 = a^2 + b^2 - 2ab*cos(C) = 10^2 + 24^2 - 2*10*24*(1/2) = 100 + 576 - 240 = 436. Thus, c = √436 = 20.
Correct Answer: A — 20
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Q. In triangle ABC, if the lengths of sides a, b, and c are 5, 12, and 13 respectively, what is the perimeter of the triangle?
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Solution
Perimeter = a + b + c = 5 + 12 + 13 = 30.
Correct Answer: B — 25
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Q. In triangle ABC, if the lengths of sides a, b, and c are 7, 24, and 25 respectively, what type of triangle is it?
A.
Acute
B.
Obtuse
C.
Right
D.
Equilateral
Show solution
Solution
Since 7² + 24² = 49 + 576 = 625 = 25², triangle ABC is a right triangle.
Correct Answer: C — Right
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Q. In triangle ABC, if the lengths of sides a, b, and c are 7, 24, and 25 respectively, what is the area of the triangle?
A.
84
B.
96
C.
120
D.
168
Show solution
Solution
Using Heron's formula, s = (7 + 24 + 25)/2 = 28. Area = √[s(s-a)(s-b)(s-c)] = √[28(28-7)(28-24)(28-25)] = √[28*21*4*3] = 84.
Correct Answer: B — 96
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Q. In triangle ABC, if the lengths of sides a, b, and c are 8, 15, and 17 respectively, what is the type of triangle?
A.
Acute
B.
Obtuse
C.
Right
D.
Equilateral
Show solution
Solution
Since 8² + 15² = 17², triangle ABC is a right triangle.
Correct Answer: C — Right
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Q. In triangle ABC, if the lengths of sides are 8 cm, 15 cm, and 17 cm, what is the type of triangle?
A.
Acute
B.
Obtuse
C.
Right
D.
Isosceles
Show solution
Solution
Since 8² + 15² = 64 + 225 = 289 = 17², triangle ABC is a right triangle.
Correct Answer: C — Right
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Q. In triangle ABC, if the lengths of the sides are 10 cm, 24 cm, and 26 cm, what is the type of triangle?
A.
Acute
B.
Obtuse
C.
Right
D.
Equilateral
Show solution
Solution
Since 10² + 24² = 100 + 576 = 676 = 26², triangle ABC is a right triangle.
Correct Answer: C — Right
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Q. In triangle ABC, if the lengths of the sides are 5, 12, and 13, what is the perimeter?
Show solution
Solution
Perimeter = a + b + c = 5 + 12 + 13 = 30.
Correct Answer: B — 25
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Q. In triangle ABC, if the lengths of the sides are 8 cm, 15 cm, and 17 cm, what is the perimeter?
A.
30 cm
B.
40 cm
C.
50 cm
D.
60 cm
Show solution
Solution
Perimeter = 8 + 15 + 17 = 40 cm.
Correct Answer: A — 30 cm
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Q. In triangle ABC, if the lengths of the sides are 8 cm, 15 cm, and 17 cm, what is the type of triangle?
A.
Acute
B.
Obtuse
C.
Right
D.
Equilateral
Show solution
Solution
Since 8² + 15² = 64 + 225 = 289 = 17², triangle ABC is a right triangle.
Correct Answer: C — Right
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Q. In triangle ABC, if the lengths of the sides are 8, 15, and 17, what is the area of the triangle?
A.
60
B.
80
C.
120
D.
150
Show solution
Solution
Using Heron's formula, the semi-perimeter s = (8 + 15 + 17)/2 = 20. Area = √[s(s-a)(s-b)(s-c)] = √[20(20-8)(20-15)(20-17)] = √[20*12*5*3] = 60.
Correct Answer: A — 60
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Q. In triangle ABC, if the lengths of the sides are 8, 15, and 17, what is the type of triangle?
A.
Acute
B.
Obtuse
C.
Right
D.
Equilateral
Show solution
Solution
Since 8² + 15² = 64 + 225 = 289 = 17², triangle ABC is a right triangle.
Correct Answer: C — Right
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Q. In triangle ABC, if the lengths of the sides are a = 5, b = 12, and c = 13, what is the perimeter of the triangle?
Show solution
Solution
The perimeter of a triangle is the sum of its sides. Therefore, perimeter = a + b + c = 5 + 12 + 13 = 30.
Correct Answer: B — 25
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Q. In triangle ABC, if the lengths of the sides are a = 8, b = 15, and c = 17, what is the perimeter?
Show solution
Solution
The perimeter of a triangle is the sum of its sides: a + b + c = 8 + 15 + 17 = 40.
Correct Answer: A — 30
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