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Mathematics for IGCSE & O level - Pythagoras' Theorem And Trigonometry (Section 2)

1
What is the formula for the area of a triangle?
Answer
(A)
½ * base * height
2
What is the formula to find the diagonal of a rectangular base?
Answer
(C)
√(a² + b²)
3
In finding lengths and angles in 3 dimensions, which of the following is the most useful?
Answer
(B)
Right-angled triangles
4
Which function is used for solving for the angle when applying the Law of Cosines?
Answer
(B)
arccosine
5
Which trigonometric function relates the adjacent side and the hypotenuse?
Answer
(B)
Cosine
6
The Pythagorean theorem applies to which type of triangle?
Answer
(C)
Right-angled
7
What type of triangles are used to determine the lengths and angles in three dimensions?
Answer
(C)
Right-angled Triangles
8
In a right triangle, which side is always the longest?
Answer
(C)
Hypotenuse
9
Given the following sides: a = 3, b = 4, c = 5. Which type of triangle do you have?
Answer
(C)
Right
10
In the formula for the area of any triangle: Area = 1/2 * ab * sinC. If you know the area and two sides, how to find the angle?
Answer
(A)
Sine^-1 (2 * Area)/(ab)
11
Which of the following is the formula to calculate the length of a diagonal of a cuboid with dimensions a, b and c?
Answer
(B)
√(a^2 + b^2 + c^2)
12
In an isosceles triangle where the lengths of two sides are equal, which of the following statements must be true?
Answer
(B)
Two angles are equal.
13
If tan(θ) = 1, what is the value of θ (in degrees)?
Answer
(B)
45
14
In the area formula, Area = 1/2 * ab * sinC. If 'a' and 'b' represent two sides, which trigonometric ratio would be used with them?
Answer
(B)
Sine
15
What value does cos(180°) evaluate to?
Answer
(C)
-1
16
Which of the following formulas correctly represents the Law of Cosines?
Answer
(A)
a^2 = b^2 + c^2 - 2bc*cosA
17
If cos(θ) = -0.5 and θ is in the second quadrant, then θ is approximately:
Answer
(C)
120°
18
If a line of sight is below the horizontal, is this considered the angle of elevation or the angle of depression?
Answer
(B)
Angle of depression
19
If KT is the height of the tree, what would you use to find the KT?
Answer
(C)
TOA
20
What is the measure of the angle of a straight line?
Answer
(B)
180 degrees
21
The angle of depression is measured from the ________.
Answer
(A)
Horizontal
22
In the context of trigonometry, what does the acronym SOHCAHTOA help you remember?
Answer
(C)
The relationship between the sides and angles of a right triangle
23
In the ambiguous case of the sine rule, when does an obtuse angle solution become impossible?
Answer
(D)
When the given angle is acute and the opposite side is shorter than one of the adjacent sides.
24
In a right triangle, if the hypotenuse is 10 and one angle is 30 degrees, what is the length of the side opposite the 30-degree angle?
Answer
(B)
5
25
What does 'SOH' stand for in SOHCAHTOA?
Answer
(A)
Sine = Opposite / Hypotenuse
26
What term describes the angle formed by a horizontal line and the line of sight to an object below?
Answer
(B)
Angle of depression
27
What is the inverse of the cosine function denoted as?
Answer
(A)
cos^-1
28
Which of the following statements correctly describe the properties of a right-angled triangle?
Answer
A
B
C
29
If sin θ = x in a right triangle, then sin(180° − θ) equals:
Answer
(B)
x
30
In a right triangle ABC, angle B is 90 degrees, and angle A is 30 degrees. If side AB is 5 cm, what is the length of side BC?
Answer
(A)
2.5 cm
31
What is the relationship between the adjacent side, opposite side, and hypotenuse in a right-angled triangle?
Answer
(C)
Adjacent² + Opposite² = Hypotenuse²
32
If in a triangle, a = 16cm, b = 10cm, and C = 150 degrees, which formula should you use to find the area?
Answer
(A)
Area = 1/2 * ab * sinC
33
What is the value of sin 90 degrees?
Answer
(B)
1
34
In a right-angled triangle, what is the sum of the two acute angles?
Answer
(D)
90 degrees
35
If a boat travels on a bearing of 090 degrees, what direction is it traveling?
Answer
(C)
East
36
In a right triangle, with respect to a given angle, which side is the 'opposite' side?
Answer
(C)
The side across from the angle
37
What is an important aspect of drawing a diagram?
Answer
(B)
Label sides and angles with the information given.
38
In triangle ABC, if a=5, b=7, and angle C = 60°, what is the length of side c (using the Law of Cosines)?
Answer
(B)
√43
39
In a right triangle, what do you call the side that is next to a specific angle (other than the hypotenuse)?
Answer
(C)
Adjacent
40
What do we call the angle of depression?
Answer
(B)
Angle between the horizontal and the line of sight to an object below.
41
The formula to use when all three sides of a triangle are given to find an angle is:
Answer
(A)
a^2 = b^2 + c^2 - 2bc cos A
42
What is the name of the function that finds the angle if you know two sides?
Answer
(A)
Inverse trigonometric function
43
In the context of non-right-angled triangles, which rule(s) is/are used for finding lengths and angles?
Answer
A
B
44
What does SOHCAHTOA help you remember?
Answer
(B)
The relationship between sides and angles.
45
If the adjacent side is 4 cm and the hypotenuse is 5 cm, what is the angle (in degrees)?
Answer
(C)
53°
46
When is the sine rule used?
Answer
(B)
When you have two sides and an angle opposite one of them.
47
Which key points should be addressed when solving problems involving trigonometry?
Answer
A
B
C
48
What is the value of cos 0 degrees?
Answer
(B)
1
49
Which trigonometric ratio is defined as Adjacent/Hypotenuse?
Answer
(B)
Cosine