Mathematics for IGCSE & O level - Pythagoras' Theorem And Trigonometry (Section 4)
1
In the context of solving triangles, if one has a right angle, which theorem should be used?
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(C)
Pythagorean Theorem
2
What is the key component that defines a three-figure bearing?
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(B)
Clockwise angle from North.
3
In a right-angled triangle, what is the side adjacent to an angle (other than the right angle)?
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(C)
The side next to the angle
4
In a diagram showing the angle of elevation and the angle of depression, which lines are considered parallel?
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(A)
The line of sight and the horizontal plane.
5
What does the angle 'C' represent in the area of triangle formula: Area = 1/2 * ab * sin C?
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(C)
The angle between sides a and b.
6
In a right-angled triangle, what is the relationship between the hypotenuse and the other two sides?
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(B)
Hypotenuse is always longer.
7
What is the primary use of the Cosine Rule?
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(B)
Relating side lengths and angles in non-right triangles.
8
If you know the lengths of all three sides of a triangle, which trigonometric rule is most appropriate for calculating the angles?
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(C)
The Cosine Rule
9
Which of the following represents a correct application of the sine rule in triangle ABC?
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(B)
sin A/a = sin B/b = sin C/c
10
Given that two sides of a triangle are 6 cm and 8 cm, and the angle between them is 60 degrees, what is the area of the triangle (rounded to one decimal place)?
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(D)
34.6 cm²
11
A ship travels 3km North and then 4km East. What distance is the ship from its starting point?
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(A)
5 km
12
A triangle has sides of length 4cm, 5cm, and 7cm. What angle would be calculated using the formula cos A = (b² + c² - a²) / (2bc)?
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(A)
The angle opposite the side of length 4 cm.
13
When finding an angle using trigonometric ratios, which other component(s) is/are necessary?
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A
B
C
D
14
If the angle of elevation from point A to the top of a building is 30 degrees, and the distance from A to the base of the building is 100 meters, what is the approximate height of the building?
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(B)
57.7 meters
15
In the formula Area = 1/2 * a * b * sin(C), which of the following does 'C' represent?
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(B)
The angle opposite side c
16
Which is the hypotenuse side in a right-angled triangle?
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(B)
The side across from the right angle
17
A ship sails from a point A on a bearing of 040 degrees for 5 km and then on a bearing of 130 degrees for 7 km. What kind of diagram is best to use to solve this problem?
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(C)
A non-right-angled triangle.
18
What does the word 'SOH' stand for in the acronym SOH CAH TOA?
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(A)
Sine = Opposite / Hypotenuse
19
Which of the following applies when dealing with the ambiguous case of the sine rule?
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A
C
20
For a triangle with sides a=5, b=8, and angle C=60 degrees, which formula is accurate for solving the length of side c?
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(A)
c² = 5² + 8² - 2*5*8*cos(60)
21
In a right-angled triangle, what is the relationship between the two acute angles?
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(C)
They are complementary
22
In order to successfully apply trigonometry to a problem, what elements should be known?
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A
B
C
D
23
What is trigonometry primarily used for?
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(B)
Relating angles and sides in triangles.
24
What does 'CAH' stand for in SOH CAH TOA?
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(B)
Cosine = Adjacent / Hypotenuse
25
If sin(θ) = 0.5, and θ is an acute angle, what is θ?
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(A)
30°
26
What is the value of tan(90°)?
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(D)
Undefined
27
In a right triangle, if you have the length of the hypotenuse and an angle (other than the right angle), what trigonometric function would you use to find the length of the side opposite the given angle?
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(B)
Sine
28
When using the Pythagorean Theorem, which side of the right triangle is represented by 'c'?
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(B)
The side opposite the right angle
29
What additional piece of information is needed to solve a triangle using the Law of Sines, when two sides and an angle are given?
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(B)
The angle opposite one of the two given sides
30
If a boat travels 3km North and then 4km East, what is the direct distance from the starting point?
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(A)
5 km
31
For acute angles, what is the relationship between sin and cos?
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(B)
sin(θ) = cos(90° - θ)
32
If side a = 7, side b = 8, and angle C = 60° in a triangle, what is the length of side c (rounded to two decimal places)?
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(A)
7.42
33
What does the abbreviation SSS mean in the context of the Cosine Rule?
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(B)
Side, Side, Side
34
In a right-angled triangle, which components are needed to find the remaining angle?
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A
B
D
35
In a right-angled triangle, what is the relationship between the sides and angles that trigonometry describes?
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(A)
The ratios of angles to side lengths.
36
If a triangle has sides 6 cm, 8 cm and the angle between these sides is 30°, what is the area of the triangle?
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(B)
12 cm²
37
If the hypotenuse of a right triangle is 13 and one leg is 5, what is the length of the other leg?
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(B)
12
38
In a right-angled triangle, what is the relationship between the hypotenuse (c) and the other two sides (a and b) as described by the Pythagorean theorem?
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(B)
c^2 = a^2 + b^2
39
If a right-angled triangle has sides of length 3 cm and 4 cm, what is the length of the hypotenuse?
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(A)
5 cm
40
What do you need to do before using the inverse trigonometric functions (sin⁻¹, cos⁻¹, tan⁻¹) on a calculator?
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(B)
Switch the calculator to degree mode.
41
What does the 'SOH' part of the mnemonic SOH CAH TOA represent?
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(B)
Sine = Opposite/Hypotenuse
42
What is the purpose of the ambiguous case when using the sine rule?
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(B)
To determine if there are zero, one, or two possible triangles
43
If you know two sides and the included angle, which trigonometric rule would be most helpful to determine the length of the third side?
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(B)
Cosine Rule
44
In the context of a right-angled triangle, what is the purpose of trigonometry?
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(B)
To relate the angles and sides of the triangle.
45
If sin(θ) = cos(θ), what must be the measure of θ (where θ is acute)?
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(C)
45°
46
Which of the following is required to calculate missing side lengths using the Pythagorean theorem?
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(A)
The lengths of two sides
47
What does the acronym 'SOH CAH TOA' represent?
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(C)
Trigonometric ratios.
48
What does the term 'opposite' refer to in a right-angled triangle, relative to a given angle?
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(B)
The side across from the angle.
49
Which statement is true about the cosine rule?
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(B)
It is used when you know two sides and the included angle, or when you know all three sides.
50
In a right-angled triangle, if you know the opposite and adjacent sides to an angle, which trigonometric function would you use to find the angle?
