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?
Răspuns
(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?
Răspuns
(B)
Cosine Rule
3
What is the defining feature of a right-angled triangle that allows the direct use of Pythagoras' theorem?
Răspuns
(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?
Răspuns
(B)
d = √(a² + b² + c²)
5
What do you need to know to calculate the third side of a right-angled triangle?
Răspuns
A
D
6
What is/are the correct ways to determine angles when using trigonometry?
Răspuns
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)?
Răspuns
(B)
Adjacent
8
What information do you need to use the cosine rule to find the length of a side?
Răspuns
(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?
Răspuns
A
B
D
10
What trigonometric function utilizes the ratio of Opposite/Adjacent?
Răspuns
(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)?
Răspuns
(C)
4.8 cm
12
Which trigonometric function uses the opposite side and the hypotenuse?
Răspuns
(A)
Sine
13
In the context of the given image, what is the significance of 'three-figure bearings'?
Răspuns
(C)
They provide a standardized way to express direction, measured from North.
14
What is the core purpose of studying trigonometry?
Răspuns
(B)
Investigating the relationships between angles and sides in triangles.
15
In order to calculate the area of a triangle, you require...
Răspuns
(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?
Răspuns
(B)
All three sides
17
Which of the following must be true for the Pythagorean theorem to apply?
Răspuns
(B)
The triangle must have one angle equal to 90 degrees.
18
What trigonometric ratio involves the opposite and hypotenuse sides?
Răspuns
(A)
Sine
19
What information is required to use the formula Area = 1/2 * ab * sin C to find the area of a triangle?
Răspuns
(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?
Răspuns
(C)
Hypotenuse
21
In a triangle ABC, if a = 10cm, b = 16cm, and C = 150°, what is the area of the triangle?
Răspuns
(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?
Răspuns
(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:
Răspuns
(C)
Trigonometry and vector addition
24
How does the area of a triangle formula using sine relate to the area of a right triangle?
Răspuns
(C)
The formula works as sin(90°) = 1.
25
Which ratio represents the sides Opposite/Hypotenuse?
Răspuns
(A)
Sine
26
What is the purpose of the 'sine' function in the context of trigonometry?
Răspuns
(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)?
Răspuns
(B)
37°
28
If two sides of a right-angled triangle are 5cm and 12cm, what is the length of the third side?
Răspuns
(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?
Răspuns
(C)
Area = 1/2 * a * b * sin(C)
30
Which of the following is a correct statement related to the area of a triangle?
Răspuns
(A)
Area of a triangle = 1/2 * base * height
31
What is the name for the longest side of a right-angled triangle?
Răspuns
(C)
Hypotenuse
32
If sin(120°) = 0.866, then sin(60°) is:
Răspuns
(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?
Răspuns
(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)?
Răspuns
(B)
5.28
35
In trigonometry, what does the acronym SOH CAH TOA help to remember?
Răspuns
(B)
The formulas for the trigonometric ratios.
36
Which of the following is the correct formula to calculate the area of a triangle?
Răspuns
(B)
Area = 1/2 * base * height
37
Which of the following statements is/are correct about trigonometry ratios?
Răspuns
B
C
38
To find the area of a triangle, using the formula 1/2 * a * b * sin C, what information is needed?
Răspuns
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?
Răspuns
(D)
5.77 meters
40
In a right-angled triangle, which side is adjacent to a given acute angle?
Răspuns
(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?
Răspuns
(C)
Using Tangent function
42
Which of the following statements are true about the sides of a right-angled triangle?
Răspuns
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?
Răspuns
(B)
57.7 m
44
What does the 'hypotenuse' of a right-angled triangle refer to?
Răspuns
(D)
Both b and c
45
What is the value of sin(30°)?
Răspuns
(B)
1/2
46
What are the steps for solving the problem of using the ratios?
Răspuns
A
B
C
D
47
What is the meaning of the 'inverse' key on the calculator when solving a trigonometry problem?
Răspuns
(B)
To find the angle
48
What is the main focus of trigonometry?
Răspuns
(B)
Studying the relationship between angles and sides in triangles.
49
In which units are trigonometric functions usually measured?
Răspuns
(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)?
