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?
Answer
(C)
North
2
What does the term 'adjacent' refer to in the context of a right triangle and a given angle?
Answer
(C)
The side next to the angle that is not the hypotenuse.
3
What does 'tan' represent in trigonometry?
Answer
(B)
Opposite/Adjacent
4
What should be the mode of the calculator be set on to calculate the angles?
Answer
(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?
Answer
(C)
Area = 1/2 * a * b * sin C
6
To use the formula Area = 1/2 * ab * sin C, which elements must be known?
Answer
A
B
7
What key elements are needed to accurately calculate the area of a triangle using the 1/2 * ab * sin C formula?
Answer
A
B
C
8
Which rule allows you to find the area of a triangle if you know two sides and the included angle?
Answer
(C)
Area = 1/2 * ab * sin C
9
To solve for angles in a right-angled triangle, you can use:
Answer
A
B
C
10
What does the abbreviation SSS represent, as it relates to using the Cosine Rule?
Answer
(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?
Answer
(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?
Answer
(A)
28.3 cm²
13
What must the sum of the two acute angles in a right-angled triangle always equal?
Answer
(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?
Answer
(B)
East
15
Which trigonometric ratio is defined as Opposite/Adjacent?
Answer
(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?
Answer
(C)
Both A and B
17
What is the relationship between the sine and cosine of complementary angles?
Answer
(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?
Answer
(B)
4
19
Which sides of a right triangle are used when calculating the tangent of an angle?
Answer
(B)
Opposite and adjacent
20
If cos θ = -0.5, and θ is between 0 and 180 degrees, what is the value of θ?
Answer
(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)?
Answer
(C)
300°
22
If you know two angles of a triangle, can you determine the third angle?
Answer
(C)
Yes, the sum of angles is 180 degrees.
23
Which statements are correct about angle calculations using trigonometric ratios?
Answer
A
B
C
24
What is the inverse function of the tangent function?
Answer
(C)
Arctangent
25
What is the result when you find the sine of an angle and then take the arcsine of that value?
Answer
(B)
The original angle
26
If sin(θ) = 0.5, what is the value of θ?
Answer
(A)
30 degrees
27
Which of the following is the Sine Rule?
Answer
(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?
Answer
A
B
D
29
In a right-angled triangle, what is the side directly across from a reference angle called?
Answer
(C)
Opposite
30
What is the relationship between a and A in the sine rule?
Answer
(A)
a is opposite angle A
31
If sin(θ) = 0.7, what is the approximate value of θ (in degrees)?
Answer
(B)
44.4°
32
If you are given the lengths of the two legs of a right triangle, how do you find the hypotenuse?
Answer
(C)
Use the Pythagorean Theorem.
33
In a right-angled triangle, the side opposite the right angle is called:
Answer
(C)
Hypotenuse
34
Which of the following statements is true about the area of a square?
Answer
(C)
Area = side * side
35
Which of the following is/are required to be known in order to solve a right-angled triangle problem?
Answer
A
B
36
Which of the following are used to solve for non-right-angled triangles?
Answer
A
B
37
What ratio does the tangent function represent?
Answer
(C)
Opposite / Adjacent
38
In the cosine rule, how do you know which angle to calculate the cos of?
Answer
(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?
Answer
A
B
40
What is needed in order to use inverse trig functions on a calculator?
Answer
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?
Answer
(B)
Pythagorean Theorem
42
In the context of 3D geometry, which theorem is most relevant for calculating lengths or angles?
Answer
(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?
Answer
(A)
40°
44
Which trigonometric functions are needed to solve non-right-angled triangles?
Answer
A
B
45
Which trigonometric ratio is used when you know two sides and want to find an angle in a right-angled triangle?
Answer
(D)
All of the above
46
What is the value of cos(30°)?
Answer
(B)
√3/2
47
In a triangle, if all three sides are known, which rule can be applied to find the angles?
Answer
(C)
Cosine Rule
48
What is the inverse function for tangent?
Answer
(C)
Arctangent
49
What is the bearing of a point that is directly west of your location?
Answer
(D)
270°
50
Which of the following describes the relationship between the sides of a right-angled triangle?
Answer
(B)
The square of the hypotenuse is equal to the sum of the squares of the other two sides.