Trigonometry Practice Questions
K-12 (Philippines) · K-12 Mathematics · 122 free MCQs with instant results and detailed explanations.
122
Total
29
Easy
64
Medium
29
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 one angle measures 45 degrees, what is the ratio of the lengths of the opposite side to the adjacent side?
A.
1:1
B.
1:โ2
C.
2:1
D.
โ2:1
Show Answer & Explanation
Correct Answer: A
In a right triangle with a 45-degree angle, the lengths of the opposite and adjacent sides are equal, giving a ratio of 1:1. This is characteristic of 45-45-90 triangles.
Q2
Easy
What is the cosine of 60 degrees?
A.
0.5
B.
1
C.
โ3/2
D.
0
Show Answer & Explanation
Correct Answer: A
The cosine of 60 degrees is 0.5, which is a fundamental value used in trigonometry, derived from the properties of special triangles.
Q3
Easy
Which of the following triangles is a right triangle?
A.
Triangle with sides 3, 4, and 5
B.
Triangle with sides 6, 8, and 10
C.
Triangle with sides 5, 12, and 13
D.
All of the above
Show Answer & Explanation
Correct Answer: D
All provided triangles follow the Pythagorean theorem (aยฒ + bยฒ = cยฒ) and are thus right triangles.
Q4
Medium
Which of the following statements is true for all angles ฮธ?
A.
sinยฒ(ฮธ) + cosยฒ(ฮธ) = 1
B.
sin(ฮธ) + cos(ฮธ) = 1
C.
tan(ฮธ) = sin(ฮธ)/cos(ฮธ)
D.
All of the above
Show Answer & Explanation
Correct Answer: A
The identity sinยฒ(ฮธ) + cosยฒ(ฮธ) = 1 holds true for all angles ฮธ, representing the Pythagorean identity.
Q5
Medium
A ladder is leaning against a wall such that the angle between the ladder and the ground is 60ยฐ. If the ladder is 10 meters long, how high does it reach on the wall?
A.
5โ3 meters
B.
10 meters
C.
5 meters
D.
8โ3 meters
Show Answer & Explanation
Correct Answer: A
Using the sine function, sin(60ยฐ) = height/10 implies height = 10 * sin(60ยฐ) = 10 * โ3/2 = 5โ3.
Q6
Medium
In a right triangle, if the adjacent side is 8 cm and the angle opposite to the side is 30ยฐ, what is the length of the opposite side?
A.
4 cm
B.
8 cm
C.
6 cm
D.
2 cm
Show Answer & Explanation
Correct Answer: A
Using the tangent function, tan(30ยฐ) = opposite/adjacent, we find opposite = adjacent * tan(30ยฐ) = 8 * (1/โ3) = 4 cm.
Q7
Medium
What is the value of sin(30ยฐ)?
A.
0.5
B.
0.866
C.
1
D.
0.707
Show Answer & Explanation
Correct Answer: A
The sine of 30 degrees is a fundamental trigonometric value which equals 0.5.
Q8
Hard
If sin(ฮธ) = 3/5, what is the value of cos(ฮธ) in the first quadrant?
A.
4/5
B.
3/5
C.
2/5
D.
1/5
Show Answer & Explanation
Correct Answer: A
In the first quadrant, we can use the Pythagorean identity sinยฒ(ฮธ) + cosยฒ(ฮธ) = 1. Given sin(ฮธ) = 3/5, we find cos(ฮธ) = โ(1 - (3/5)ยฒ) = โ(1 - 9/25) = โ(16/25) = 4/5.
Q9
Hard
In triangle ABC, angle A measures 30 degrees and angle B measures 60 degrees. What is the length of side a, opposite angle A, if side b, opposite angle B, is known to be 10 units?
A.
5โ3
B.
10
C.
5
D.
5โ2
Show Answer & Explanation
Correct Answer: A
Using the Law of Sines: a/sin(A) = b/sin(B). Substituting the values, we have a/sin(30) = 10/sin(60). Solving gives a = 5โ3.
Q10
Hard
A ladder leans against a wall making an angle of 75 degrees with the ground. If the foot of the ladder is 3 meters away from the wall, how long is the ladder?
A.
3/โ(3-โ3)
B.
6
C.
12/โ3
D.
3โ3
Show Answer & Explanation
Correct Answer: C
Using the cosine function: cos(75) = adjacent/hypotenuse. The adjacent side is 3, so hypotenuse (ladder length) = 3/cos(75). After calculating cos(75), we find the ladder length to be 12/โ3.
Showing 10 of 122 questions. Start a quiz to practice all questions with scoring and timer.
Practice All 122 Questions →Other K-12 (Philippines) Subjects
Trigonometry โ K-12 (Philippines) K-12 Mathematics Practice Questions Online
This page contains 122 practice MCQs for the chapter Trigonometry in K-12 (Philippines) K-12 Mathematics. The questions are organized by difficulty โ 29 easy, 64 medium, 29 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.