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