Q. In triangle ABC, if AB = 8 cm, AC = 6 cm, and angle A = 60 degrees, what is the length of side BC using the Law of Cosines?
A.
10 cm
B.
8 cm
C.
7 cm
D.
5 cm
Show solution
Solution
Using the Law of Cosines: BC^2 = AB^2 + AC^2 - 2 * AB * AC * cos(A) = 8^2 + 6^2 - 2 * 8 * 6 * (1/2) = 64 + 36 - 48 = 52. Therefore, BC = √52 = 10 cm.
Correct Answer:
A
— 10 cm
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Q. In triangle ABC, if AB = AC and angle A = 100 degrees, what is the measure of angles B and C?
A.
40 degrees each
B.
50 degrees each
C.
60 degrees each
D.
80 degrees each
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Solution
In an isosceles triangle, angles B and C are equal. Therefore, angle B = angle C = (180 - 100) / 2 = 40 degrees.
Correct Answer:
A
— 40 degrees each
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Q. In triangle ABC, if AB = AC and angle A = 40 degrees, what are the measures of angles B and C?
A.
70 degrees each
B.
80 degrees each
C.
40 degrees each
D.
60 degrees each
Show solution
Solution
Since AB = AC, angles B and C are equal. Therefore, angle B + angle C = 140 degrees, and each angle is 70 degrees.
Correct Answer:
B
— 80 degrees each
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Q. In triangle ABC, if AB = AC and angle A = 40 degrees, what is the measure of angles B and C?
A.
70 degrees each
B.
80 degrees each
C.
60 degrees each
D.
50 degrees each
Show solution
Solution
Since AB = AC, angles B and C are equal. Therefore, angle B + angle C = 180 - 40 = 140 degrees, so each angle is 70 degrees.
Correct Answer:
B
— 80 degrees each
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Q. In triangle ABC, if AB = AC and angle A = 40°, what is the measure of angle B?
A.
40°
B.
70°
C.
80°
D.
60°
Show solution
Solution
In an isosceles triangle, the base angles are equal. Therefore, angle B = angle C. Since the sum of angles in a triangle is 180°, we have 40° + 2B = 180°, leading to B = 70°.
Correct Answer:
B
— 70°
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Q. In triangle ABC, if angle A = 30 degrees and angle B = 60 degrees, what is angle C?
A.
30 degrees
B.
60 degrees
C.
90 degrees
D.
120 degrees
Show solution
Solution
Angle C can be found by subtracting the sum of angles A and B from 180 degrees: 180 - (30 + 60) = 90 degrees.
Correct Answer:
C
— 90 degrees
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Q. In triangle ABC, if angle A = 30 degrees and angle B = 60 degrees, what is the length of side a opposite angle A if side b = 10?
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Solution
Using the sine rule: a/sin(A) = b/sin(B) => a = b * sin(A)/sin(B) = 10 * sin(30)/sin(60) = 10 * 0.5/(√3/2) = 5.
Correct Answer:
A
— 5
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Q. In triangle ABC, if angle A = 30 degrees and angle B = 70 degrees, what is the measure of angle C?
A.
30 degrees
B.
40 degrees
C.
50 degrees
D.
80 degrees
Show solution
Solution
The sum of angles in a triangle is 180 degrees. Therefore, angle C = 180 - 30 - 70 = 80 degrees.
Correct Answer:
C
— 50 degrees
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Q. In triangle ABC, if angle A = 30° and angle B = 60°, what is angle C?
A.
90°
B.
60°
C.
30°
D.
120°
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Solution
Angle C = 180° - (angle A + angle B) = 180° - (30° + 60°) = 90°.
Correct Answer:
A
— 90°
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Q. In triangle ABC, if angle A = 40 degrees and angle B = 60 degrees, what is the measure of angle C?
A.
80 degrees
B.
100 degrees
C.
120 degrees
D.
140 degrees
Show solution
Solution
The sum of angles in a triangle is 180 degrees. Therefore, angle C = 180 - 40 - 60 = 80 degrees.
Correct Answer:
A
— 80 degrees
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Q. In triangle ABC, if angle A = 45 degrees and angle B = 45 degrees, what type of triangle is ABC?
A.
Scalene
B.
Isosceles
C.
Equilateral
D.
Right
Show solution
Solution
Since two angles are equal (45 degrees each), triangle ABC is an isosceles triangle.
Correct Answer:
B
— Isosceles
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Q. In triangle ABC, if angle A = 45 degrees and angle B = 45 degrees, what type of triangle is it?
A.
Equilateral
B.
Isosceles
C.
Scalene
D.
Right-angled
Show solution
Solution
Triangle ABC is isosceles because two angles are equal.
Correct Answer:
B
— Isosceles
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Q. In triangle ABC, if angle A = 45 degrees and angle B = 55 degrees, what is the measure of angle C?
A.
80 degrees
B.
90 degrees
C.
100 degrees
D.
70 degrees
Show solution
Solution
The sum of angles in a triangle is 180 degrees. Therefore, angle C = 180 - (45 + 55) = 80 degrees.
Correct Answer:
A
— 80 degrees
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Q. In triangle ABC, if angle A = 45 degrees, angle B = 45 degrees, and side a = 10 cm, what is the length of side c?
A.
10 cm
B.
10√2 cm
C.
5√2 cm
D.
20 cm
Show solution
Solution
In an isosceles right triangle, the sides opposite the 45-degree angles are equal. Thus, c = a√2 = 10√2 cm.
Correct Answer:
B
— 10√2 cm
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Q. In triangle ABC, if angle A = 50 degrees and angle B = 60 degrees, what is angle C?
A.
70 degrees
B.
80 degrees
C.
90 degrees
D.
100 degrees
Show solution
Solution
The sum of the angles in a triangle is 180 degrees. Therefore, angle C = 180 - (50 + 60) = 70 degrees.
Correct Answer:
B
— 80 degrees
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Q. In triangle ABC, if angle A = 50 degrees and angle B = 60 degrees, what is the measure of angle C?
A.
70 degrees
B.
80 degrees
C.
90 degrees
D.
100 degrees
Show solution
Solution
The sum of angles in a triangle is 180 degrees. Angle C = 180 - (50 + 60) = 70 degrees.
Correct Answer:
B
— 80 degrees
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Q. In triangle ABC, if angle A = 50 degrees and angle B = 70 degrees, what is the measure of angle C?
A.
60 degrees
B.
70 degrees
C.
80 degrees
D.
90 degrees
Show solution
Solution
Angle C can be calculated as 180 - (50 + 70) = 60 degrees.
Correct Answer:
C
— 80 degrees
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Q. In triangle ABC, if angle A = 50° and angle B = 60°, what is 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°. Therefore, angle C = 180° - 50° - 60° = 70°.
Correct Answer:
C
— 70 degrees
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Q. In triangle ABC, if angle A = 50° and angle B = 60°, what is the measure of angle C?
A.
70°
B.
80°
C.
90°
D.
100°
Show solution
Solution
The sum of angles in a triangle is 180°. Therefore, angle C = 180° - (50° + 60°) = 70°.
Correct Answer:
A
— 70°
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Q. In triangle ABC, if angle A = 60 degrees, angle B = 70 degrees, and side a = 10 cm, what is the length of side b using the Law of Sines?
A.
8.66 cm
B.
9.15 cm
C.
7.84 cm
D.
10.00 cm
Show solution
Solution
Using the Law of Sines: a/sin(A) = b/sin(B). Thus, b = a * (sin(B)/sin(A)) = 10 * (sin(70)/sin(60)). Calculating gives b ≈ 10 * (0.9397/0.8660) ≈ 10.80 cm.
Correct Answer:
B
— 9.15 cm
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Q. In triangle ABC, if angle A = 60° and angle B = 70°, what is the measure of angle C?
A.
50°
B.
60°
C.
70°
D.
80°
Show solution
Solution
The sum of angles in a triangle is 180°. Therefore, angle C = 180° - (60° + 70°) = 180° - 130° = 50°.
Correct Answer:
A
— 50°
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Q. In triangle ABC, if angle A = 90 degrees and AB = 6 cm, AC = 8 cm, what is the length of BC?
A.
10 cm
B.
12 cm
C.
14 cm
D.
16 cm
Show solution
Solution
Using the Pythagorean theorem: BC = √(AB² + AC²) = √(6² + 8²) = √(36 + 64) = √100 = 10 cm.
Correct Answer:
A
— 10 cm
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Q. In triangle ABC, if angle A = 90 degrees and AB = AC, what type of triangle is ABC?
A.
Scalene
B.
Isosceles
C.
Equilateral
D.
Right
Show solution
Solution
Triangle ABC is an isosceles right triangle because it has two equal sides and one right angle.
Correct Answer:
B
— Isosceles
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Q. In triangle ABC, if angle A = 90 degrees, angle B = 45 degrees, what is the measure of angle C?
A.
45 degrees
B.
60 degrees
C.
30 degrees
D.
90 degrees
Show solution
Solution
The sum of angles in a triangle is 180 degrees. Therefore, angle C = 180 - 90 - 45 = 45 degrees.
Correct Answer:
A
— 45 degrees
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Q. In triangle ABC, if angle A is 40 degrees and angle B is 60 degrees, what is the measure of angle C?
A.
80 degrees
B.
100 degrees
C.
40 degrees
D.
60 degrees
Show solution
Solution
The sum of angles in a triangle is 180 degrees. Therefore, angle C = 180 - (40 + 60) = 80 degrees.
Correct Answer:
A
— 80 degrees
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Q. In triangle ABC, if angle A is 50 degrees and angle B is 60 degrees, what is the measure of angle C?
A.
70 degrees
B.
80 degrees
C.
90 degrees
D.
100 degrees
Show solution
Solution
The sum of angles in a triangle is 180 degrees. Therefore, angle C = 180 - (50 + 60) = 70 degrees.
Correct Answer:
A
— 70 degrees
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Q. In triangle ABC, if angle A is 50 degrees and angle B is 70 degrees, what is the measure of angle C?
A.
60 degrees
B.
70 degrees
C.
80 degrees
D.
90 degrees
Show solution
Solution
The sum of angles in a triangle is 180 degrees. Therefore, angle C = 180 - (50 + 70) = 60 degrees.
Correct Answer:
C
— 80 degrees
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Q. In triangle ABC, if angle A is 60 degrees and angle B is 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 is 60 degrees and angle B is 90 degrees, what is the measure of angle C?
A.
30 degrees
B.
60 degrees
C.
90 degrees
D.
120 degrees
Show solution
Solution
The sum of angles in a triangle is 180 degrees. Therefore, angle C = 180 - (60 + 90) = 30 degrees.
Correct Answer:
A
— 30 degrees
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Q. In triangle ABC, if the lengths of sides AB and AC are equal, what type of triangle is ABC?
A.
Scalene
B.
Isosceles
C.
Equilateral
D.
Right
Show solution
Solution
A triangle with two equal sides is classified as an isosceles triangle.
Correct Answer:
B
— Isosceles
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