Trigonometry Practice Questions
IGCSE (Cambridge) · IGCSE Mathematics · 130 free MCQs with instant results and detailed explanations.
130
Total
34
Easy
72
Medium
24
Hard
Start Practicing Trigonometry
Take a timed quiz or customize your practice session
Sample Questions from Trigonometry
Here are 10 sample questions. Start a quiz to get randomized questions with scoring.
Q1
Easy
In a right triangle, if the length of the opposite side is 4 units and the length of the hypotenuse is 5 units, what is the value of sin(ฮธ)?
A.
0.8
B.
0.6
C.
0.5
D.
0.4
Show Answer & Explanation
Correct Answer: A
Sine is defined as the length of the opposite side divided by the length of the hypotenuse. Therefore, sin(ฮธ) = 4/5 = 0.8.
Q2
Easy
In a right triangle, if the angle A is 30 degrees and the length of the opposite side is 5 cm, what is the length of the hypotenuse?
A.
10 cm
B.
5 cm
C.
8.66 cm
D.
6 cm
Show Answer & Explanation
Correct Answer: A
Using the sine function, sin(30ยฐ) = opposite/hypotenuse. Here, sin(30ยฐ) = 1/2, so 1/2 = 5/hypotenuse. Solving gives hypotenuse = 10 cm.
Q3
Easy
In a right triangle, if the adjacent side to angle B measures 8 cm and the angle B is 45 degrees, what is the length of the opposite side?
A.
8 cm
B.
6.36 cm
C.
5.66 cm
D.
10 cm
Show Answer & Explanation
Correct Answer: A
In a 45-degree angle triangle, the opposite and adjacent sides are equal. Therefore, the opposite side is also 8 cm.
Q4
Medium
In a right triangle, if angle A is 30 degrees and side a (opposite angle A) is 5 cm, what is the length of side c (hypotenuse)?
A.
10 cm
B.
5 cm
C.
8.66 cm
D.
4.33 cm
Show Answer & Explanation
Correct Answer: A
In a right triangle with an angle of 30 degrees, the hypotenuse is twice the length of the side opposite to the angle. Here, side a is 5 cm, so side c (hypotenuse) is 5 cm * 2 = 10 cm.
Q5
Medium
What is the sine of an angle that has a cosine of 0.6 in a right triangle?
A.
0.8
B.
0.6
C.
0.5
D.
0.3
Show Answer & Explanation
Correct Answer: A
Using the Pythagorean identity sinยฒ(ฮธ) + cosยฒ(ฮธ) = 1, where cos(ฮธ) = 0.6, we have sinยฒ(ฮธ) = 1 - (0.6)ยฒ = 1 - 0.36 = 0.64, thus sin(ฮธ) = โ0.64 = 0.8.
Q6
Medium
A ladder leans against a wall making an angle of 60 degrees with the ground. If the foot of the ladder is 4 m away from the wall, how long is the ladder?
A.
4 m
B.
8 m
C.
2 m
D.
5 m
Show Answer & Explanation
Correct Answer: B
Using the cosine function, cos(60ยฐ) = adjacent/hypotenuse = 4/h, we find h = 4/cos(60ยฐ). Since cos(60ยฐ) = 0.5, we have h = 4/0.5 = 8 m.
Q7
Medium
If tan(ฮธ) = 3/4, what is sin(ฮธ) in simplest form?
A.
3/5
B.
4/5
C.
5/4
D.
1/5
Show Answer & Explanation
Correct Answer: A
In a right triangle where tan(ฮธ) = opposite/adjacent = 3/4, by the Pythagorean theorem, the hypotenuse is โ(3ยฒ + 4ยฒ) = 5. Therefore, sin(ฮธ) = opposite/hypotenuse = 3/5.
Q8
Hard
In triangle ABC, angle A is 30 degrees, and side a (opposite angle A) is 10 cm. Calculate the length of side b (opposite angle B) if angle B measures 60 degrees. Use the sine rule.
A.
15 cm
B.
8.66 cm
C.
5 cm
D.
12 cm
Show Answer & Explanation
Correct Answer: B
Using the sine rule, a/sin(A) = b/sin(B). Substituting the values gives 10/sin(30) = b/sin(60). Solving yields b = 8.66 cm.
Q9
Hard
In a right triangle, if angle A is 30 degrees and side opposite to angle A measures 5 cm, what is the length of the hypotenuse?
A.
10 cm
B.
5โ3 cm
C.
5 cm
D.
10โ3 cm
Show Answer & Explanation
Correct Answer: A
In a right triangle, the sine of an angle is equal to the opposite side divided by the hypotenuse. For angle A = 30ยฐ, sin(30ยฐ) = 0.5. Therefore, if the opposite side is 5 cm, hypotenuse = 5 / sin(30ยฐ) = 5 / 0.5 = 10 cm.
Q10
Hard
A ladder is leaning against a wall, making an angle of 60 degrees with the ground. If the foot of the ladder is 3 meters from the wall, how long is the ladder?
A.
3โ3 m
B.
6 m
C.
3 m
D.
6โ3 m
Show Answer & Explanation
Correct Answer: B
Using trigonometric relationships in right triangles, the cosine of the angle gives the adjacent side (distance from wall) divided by the hypotenuse (length of the ladder). cos(60ยฐ) = adjacent/hypotenuse = 3/hypotenuse. Thus, hypotenuse = 3/cos(60ยฐ) = 3/(1/2) = 6 m.
Showing 10 of 130 questions. Start a quiz to practice all questions with scoring and timer.
Practice All 130 Questions →Other IGCSE (Cambridge) Subjects
Trigonometry โ IGCSE (Cambridge) IGCSE Mathematics Practice Questions Online
This page contains 130 practice MCQs for the chapter Trigonometry in IGCSE (Cambridge) IGCSE Mathematics. The questions are organized by difficulty โ 34 easy, 72 medium, 24 hard โ so you can choose the right level for your preparation.
Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.