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