Mathematics for IGCSE & O level - Pythagoras' Theorem And Trigonometry (Section 7)
1
When using a three-figure bearing, which direction is the reference point for measuring the angle?
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(C)
North
2
What does the term 'adjacent' refer to in the context of a right triangle and a given angle?
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(C)
The side next to the angle that is not the hypotenuse.
3
What does 'tan' represent in trigonometry?
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(B)
Opposite/Adjacent
4
What should be the mode of the calculator be set on to calculate the angles?
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(B)
Deg
5
What is the appropriate formula to use, to calculate the area of a triangle when the length of two sides and an included angle are given?
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(C)
Area = 1/2 * a * b * sin C
6
To use the formula Area = 1/2 * ab * sin C, which elements must be known?
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A
B
7
What key elements are needed to accurately calculate the area of a triangle using the 1/2 * ab * sin C formula?
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A
B
C
8
Which rule allows you to find the area of a triangle if you know two sides and the included angle?
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(C)
Area = 1/2 * ab * sin C
9
To solve for angles in a right-angled triangle, you can use:
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A
B
C
10
What does the abbreviation SSS represent, as it relates to using the Cosine Rule?
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(A)
Side Side Side
11
A ship travels from point A on a bearing of 000 degrees for 6 km, and then 090 degrees for 8 km. How can we determine the distance the ship is from the starting point?
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(C)
Pythagorean Theorem
12
If you have a triangle with sides 8 cm, 10 cm, and an included angle of 45 degrees, what is the area?
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(A)
28.3 cm²
13
What must the sum of the two acute angles in a right-angled triangle always equal?
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(C)
90 degrees
14
If the bearing of point B from point A is 090 degrees, which direction is point B in relation to A?
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(B)
East
15
Which trigonometric ratio is defined as Opposite/Adjacent?
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(C)
Tangent
16
If the height of a tower and the angle of elevation from a point on the ground to the top of the tower are known, what can be determined?
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(C)
Both A and B
17
What is the relationship between the sine and cosine of complementary angles?
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(A)
They are equal.
18
If a right triangle has a hypotenuse of 10 and one leg of 8, what is the length of the other leg?
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(B)
4
19
Which sides of a right triangle are used when calculating the tangent of an angle?
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(B)
Opposite and adjacent
20
If cos θ = -0.5, and θ is between 0 and 180 degrees, what is the value of θ?
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(C)
120°
21
If the bearing of point B from point A is 120°, what is the bearing of point A from point B (approximately)?
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(C)
300°
22
If you know two angles of a triangle, can you determine the third angle?
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(C)
Yes, the sum of angles is 180 degrees.
23
Which statements are correct about angle calculations using trigonometric ratios?
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A
B
C
24
What is the inverse function of the tangent function?
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(C)
Arctangent
25
What is the result when you find the sine of an angle and then take the arcsine of that value?
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(B)
The original angle
26
If sin(θ) = 0.5, what is the value of θ?
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(A)
30 degrees
27
Which of the following is the Sine Rule?
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(C)
a/sin A = b/sin B = c/sin C
28
What can be determined by knowing the measurements of the angles in a triangle, and the lengths of the sides of a right-angled triangle?
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A
B
D
29
In a right-angled triangle, what is the side directly across from a reference angle called?
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(C)
Opposite
30
What is the relationship between a and A in the sine rule?
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(A)
a is opposite angle A
31
If sin(θ) = 0.7, what is the approximate value of θ (in degrees)?
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(B)
44.4°
32
If you are given the lengths of the two legs of a right triangle, how do you find the hypotenuse?
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(C)
Use the Pythagorean Theorem.
33
In a right-angled triangle, the side opposite the right angle is called:
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(C)
Hypotenuse
34
Which of the following statements is true about the area of a square?
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(C)
Area = side * side
35
Which of the following is/are required to be known in order to solve a right-angled triangle problem?
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A
B
36
Which of the following are used to solve for non-right-angled triangles?
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A
B
37
What ratio does the tangent function represent?
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(C)
Opposite / Adjacent
38
In the cosine rule, how do you know which angle to calculate the cos of?
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(A)
The angle opposite the longest side.
39
Which of the following are necessary to calculate the area of a non-right triangle using the formula Area = 1/2 * ab * sin C?
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A
B
40
What is needed in order to use inverse trig functions on a calculator?
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A
C
41
If a boat sails 6km on a bearing of 000 degrees (North) and then 8km on a bearing of 090 degrees (East), which theorem would you use to calculate the distance from the starting point?
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(B)
Pythagorean Theorem
42
In the context of 3D geometry, which theorem is most relevant for calculating lengths or angles?
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(D)
Both b and c
43
The angle of depression from a point A to a point B is 40°. What is the angle of elevation from B to A?
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(A)
40°
44
Which trigonometric functions are needed to solve non-right-angled triangles?
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A
B
45
Which trigonometric ratio is used when you know two sides and want to find an angle in a right-angled triangle?
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(D)
All of the above
46
What is the value of cos(30°)?
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(B)
√3/2
47
In a triangle, if all three sides are known, which rule can be applied to find the angles?
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(C)
Cosine Rule
48
What is the inverse function for tangent?
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(C)
Arctangent
49
What is the bearing of a point that is directly west of your location?
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(D)
270°
50
Which of the following describes the relationship between the sides of a right-angled triangle?
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(B)
The square of the hypotenuse is equal to the sum of the squares of the other two sides.
