Mathematics for IGCSE & O level - Pythagoras' Theorem And Trigonometry (Section 1)
1
Which trigonometric ratio is used to find the angle when you know the adjacent and the hypotenuse sides?
Trả lời
(B)
Cosine
2
In a triangle, if you know the lengths of two sides and the included angle, which rule would you likely use to find the length of the third side?
Trả lời
(B)
Cosine Rule
3
What is the defining feature of a right-angled triangle that allows the direct use of Pythagoras' theorem?
Trả lời
(B)
It has one angle that is 90 degrees.
4
What is the formula for calculating the length of the diagonal of a cuboid with sides a, b, and c?
Trả lời
(B)
d = √(a² + b² + c²)
5
What do you need to know to calculate the third side of a right-angled triangle?
Trả lời
A
D
6
What is/are the correct ways to determine angles when using trigonometry?
Trả lời
A
B
D
7
What is the name given to the side of the triangle next to a given angle (that is not the hypotenuse)?
Trả lời
(B)
Adjacent
8
What information do you need to use the cosine rule to find the length of a side?
Trả lời
(C)
Two sides and the included angle.
9
In a three-dimensional problem involving finding lengths or angles, which of the following is/are useful tools?
Trả lời
A
B
D
10
What trigonometric function utilizes the ratio of Opposite/Adjacent?
Trả lời
(C)
Tangent
11
If two sides of a triangle measure 5 cm and 8 cm, and the included angle is 60 degrees, what is the length of the third side (approximate)?
Trả lời
(C)
4.8 cm
12
Which trigonometric function uses the opposite side and the hypotenuse?
Trả lời
(A)
Sine
13
In the context of the given image, what is the significance of 'three-figure bearings'?
Trả lời
(C)
They provide a standardized way to express direction, measured from North.
14
What is the core purpose of studying trigonometry?
Trả lời
(B)
Investigating the relationships between angles and sides in triangles.
15
In order to calculate the area of a triangle, you require...
Trả lời
(A)
base & height or 2 sides and the included angle
16
What do you need to know to use the cosine rule to find an angle in a triangle?
Trả lời
(B)
All three sides
17
Which of the following must be true for the Pythagorean theorem to apply?
Trả lời
(B)
The triangle must have one angle equal to 90 degrees.
18
What trigonometric ratio involves the opposite and hypotenuse sides?
Trả lời
(A)
Sine
19
What information is required to use the formula Area = 1/2 * ab * sin C to find the area of a triangle?
Trả lời
(B)
The length of two sides and the angle between them.
20
In a right-angled triangle, what do you call the side *opposite* the right angle?
Trả lời
(C)
Hypotenuse
21
In a triangle ABC, if a = 10cm, b = 16cm, and C = 150°, what is the area of the triangle?
Trả lời
(A)
40 cm²
22
Which of the following is correct regarding the angle of elevation and angle of depression in the same diagram, assuming parallel lines?
Trả lời
(C)
Angle of elevation equals the angle of depression.
23
A boat sails 10 km due north and then 8 km in a south-easterly direction. To determine the final position of the boat you will need to consider:
Trả lời
(C)
Trigonometry and vector addition
24
How does the area of a triangle formula using sine relate to the area of a right triangle?
Trả lời
(C)
The formula works as sin(90°) = 1.
25
Which ratio represents the sides Opposite/Hypotenuse?
Trả lời
(A)
Sine
26
What is the purpose of the 'sine' function in the context of trigonometry?
Trả lời
(A)
To relate angles to side lengths in a right triangle.
27
If sin(x) = 0.6, what is the approximate value of x (in degrees)?
Trả lời
(B)
37°
28
If two sides of a right-angled triangle are 5cm and 12cm, what is the length of the third side?
Trả lời
(A)
13 cm
29
If the angle between sides a and b of a triangle is known, along with the lengths of sides a and b, which formula can be used to calculate the triangle's area?
Trả lời
(C)
Area = 1/2 * a * b * sin(C)
30
Which of the following is a correct statement related to the area of a triangle?
Trả lời
(A)
Area of a triangle = 1/2 * base * height
31
What is the name for the longest side of a right-angled triangle?
Trả lời
(C)
Hypotenuse
32
If sin(120°) = 0.866, then sin(60°) is:
Trả lời
(B)
0.866
33
Which trigonometric function can be used if given the lengths of all three sides and you are trying to find an angle?
Trả lời
(C)
Cosine
34
If a triangle has sides a = 4, b = 6, and angle C = 60 degrees, what is the length of side c (approximately)?
Trả lời
(B)
5.28
35
In trigonometry, what does the acronym SOH CAH TOA help to remember?
Trả lời
(B)
The formulas for the trigonometric ratios.
36
Which of the following is the correct formula to calculate the area of a triangle?
Trả lời
(B)
Area = 1/2 * base * height
37
Which of the following statements is/are correct about trigonometry ratios?
Trả lời
B
C
38
To find the area of a triangle, using the formula 1/2 * a * b * sin C, what information is needed?
Trả lời
A
B
39
If the height of a tree is 10 meters and the angle of elevation from a point on the ground to the top of the tree is 60 degrees, what is the approximate distance from the observer to the base of the tree?
Trả lời
(D)
5.77 meters
40
In a right-angled triangle, which side is adjacent to a given acute angle?
Trả lời
(C)
The side next to the angle (other than the hypotenuse).
41
If the angle of elevation is given and the height of an object is known, how can you find the horizontal distance to the object?
Trả lời
(C)
Using Tangent function
42
Which of the following statements are true about the sides of a right-angled triangle?
Trả lời
A
C
43
The angle of elevation from point A to the top of a tower is 30°. The distance from A to the tower's base is 100m. What is the tower's approximate height?
Trả lời
(B)
57.7 m
44
What does the 'hypotenuse' of a right-angled triangle refer to?
Trả lời
(D)
Both b and c
45
What is the value of sin(30°)?
Trả lời
(B)
1/2
46
What are the steps for solving the problem of using the ratios?
Trả lời
A
B
C
D
47
What is the meaning of the 'inverse' key on the calculator when solving a trigonometry problem?
Trả lời
(B)
To find the angle
48
What is the main focus of trigonometry?
Trả lời
(B)
Studying the relationship between angles and sides in triangles.
49
In which units are trigonometric functions usually measured?
Trả lời
(C)
Degrees or Radians
50
If two sides of a triangle are 7 cm and 9 cm, and the included angle is 60 degrees, what is the length of the third side (approximately)?
