Trigonometri Practice Questions
UN (Indonesia) · UN Matematika · 123 free MCQs with instant results and detailed explanations.
123
Total
30
Easy
66
Medium
27
Hard
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Sample Questions from Trigonometri
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Q1
Easy
In a right triangle, if the opposite side is 3 and the hypotenuse is 5, what is the value of sin(ฮธ)?
A.
0.6
B.
0.8
C.
0.5
D.
0.75
Show Answer & Explanation
Correct Answer: A
The sine of an angle is the ratio of the opposite side to the hypotenuse, so sin(ฮธ) = 3/5 = 0.6.
Q2
Easy
What is the value of sin(30ยฐ)?
A.
0.5
B.
1
C.
0.866
D.
0.707
Show Answer & Explanation
Correct Answer: A
The sine of 30 degrees is known to be 0.5 from trigonometric values of standard angles.
Q3
Easy
In a right triangle, if one angle is 60ยฐ and the hypotenuse is 10 units, what is the length of the opposite side?
A.
5โ3
B.
10
C.
5
D.
8.66
Show Answer & Explanation
Correct Answer: A
The length of the opposite side can be found using the formula: opposite = hypotenuse * sin(ฮธ); here, opposite = 10 * sin(60ยฐ) = 10 * (โ3/2) = 5โ3.
Q4
Medium
In a right triangle, if angle A measures 30 degrees and side a (opposite to angle A) is 5 cm, what is the length of the hypotenuse?
A.
10 cm
B.
5 cm
C.
8.66 cm
D.
7.5 cm
Show Answer & Explanation
Correct Answer: A
Using the sine function, sin(30ยฐ) = opposite/hypotenuse, we calculate hypotenuse = opposite/sin(30ยฐ) = 5/sin(30ยฐ) = 5/(0.5) = 10 cm.
Q5
Medium
A ladder is leaning against a wall, forming a 60-degree angle with the ground. If the base of the ladder is 4 meters from the wall, how tall is the ladder?
A.
8 m
B.
4โ3 m
C.
2โ3 m
D.
6 m
Show Answer & Explanation
Correct Answer: B
In this scenario, using the cosine function: base = hypotenuse * cos(60ยฐ). Let hypotenuse be 'h', then 4 = h * (1/2) gives h = 8 m. The height is given by: height = h * sin(60ยฐ) = 8 * (โ3/2) = 4โ3 m.
Q6
Medium
Which of the following angles has a sine value equal to the cosine value of its complementary angle?
A.
30ยฐ
B.
45ยฐ
C.
60ยฐ
D.
90ยฐ
Show Answer & Explanation
Correct Answer: B
By definition, sin(ฮธ) = cos(90ยฐ - ฮธ). For ฮธ = 45ยฐ, sin(45ยฐ) = cos(45ยฐ) = โ2/2, confirming the equality.
Q7
Medium
If tan(ฮธ) = 0.5, what is the value of sin(ฮธ)?
A.
1/โ5
B.
2/โ5
C.
1/2
D.
โ3/2
Show Answer & Explanation
Correct Answer: A
Using the identity tan(ฮธ) = sin(ฮธ)/cos(ฮธ) and knowing tan(ฮธ) = 0.5, we can derive the values of sin(ฮธ) and cos(ฮธ) to find sin(ฮธ) = 1/โ5.
Q8
Hard
In a right triangle, if the angle A is 30 degrees and the length of the hypotenuse is 10 cm, what is the length of the opposite side to angle A?
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
Show Answer & Explanation
Correct Answer: A
The length of the opposite side can be calculated using the sine function: sin(A) = opposite/hypotenuse. For angle A = 30 degrees, sin(30) = 0.5. Therefore, opposite = hypotenuse * sin(A) = 10 * 0.5 = 5 cm.
Q9
Hard
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 b (adjacent to angle A)?
A.
8.66 cm
B.
10 cm
C.
5 cm
D.
7.5 cm
Show Answer & Explanation
Correct Answer: A
Using the tangent function, tan(A) = opposite/adjacent. Here, tan(30ยฐ) = 1/โ3, thus the adjacent side is a/tan(30ยฐ) which gives us 5 * โ3 = 8.66 cm.
Q10
Hard
In a right triangle, if angle A is 30 degrees and side opposite to angle A is 5 cm, what is the length of the hypotenuse?
A.
10 cm
B.
5โ3 cm
C.
5 cm
D.
25 cm
Show Answer & Explanation
Correct Answer: A
In a right triangle, the sine of angle A (30 degrees) is equal to the opposite side (5 cm) divided by the hypotenuse. Since sin(30ยฐ) = 0.5, we have 0.5 = 5 / hypotenuse. Solving this gives hypotenuse = 10 cm.
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Trigonometri โ UN (Indonesia) UN Matematika Practice Questions Online
This page contains 123 practice MCQs for the chapter Trigonometri in UN (Indonesia) UN Matematika. The questions are organized by difficulty โ 30 easy, 66 medium, 27 hard โ so you can choose the right level for your preparation.
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