Mathematics for IGCSE & O level - Pythagoras' Theorem And Trigonometry (Section 1)
1
In triangle ABC, where a = 7, b = 5 and C = 60°. Find the value of c.
Answer
(B)
√39
2
Which formula is most applicable if you want to calculate the area of a triangle if you know the lengths of two sides and an angle?
Answer
(B)
A = 1/2 * a * b * sin C
3
In a right triangle, what is the relationship between the acute angles?
Answer
(B)
They are complementary
4
Which of the following is a correct application of the Pythagorean theorem?
Answer
(B)
a^2 + b^2 = c^2
5
What is the first step when attempting the question: A boat, C, is 10km away on a bearing of 090 degrees from a starting point K. Boat B is 6km away on a bearing of 150 degrees?
Answer
(B)
Draw a diagram
6
In a right-angled triangle, which side is opposite the right angle?
Answer
(C)
Hypotenuse
7
Consider a parallelogram with sides of length 5cm and 11cm, and the angle between adjacent sides is 30 degrees. Which trigonometric rule or formula would you use to find the area?
Answer
(D)
Area of a parallelogram = ab*sinC
8
Which of the following functions is positive in the third quadrant?
Answer
(C)
tan
9
Given a rectangular box, to find the diagonal from one corner through the box to the opposite corner, what method is used?
Answer
(A)
Pythagoras Theorem
10
If A boat, C, is 20m north of point K, and the angle of elevation to the top of the tree T from C is 15 degrees, how is the height of the tree, KT, calculated?
Answer
(A)
Tan
11
If a boat sails 10 km on a bearing of 030° and then 15 km on a bearing of 120°, which formula can be used to find the direct distance from the starting point?
Answer
(C)
Cosine Rule
12
The angle of elevation and angle of depression are equal because:
Answer
(C)
They are alternate interior angles
13
Consider a triangle with sides a, b, and c, and angle A opposite side a. According to the cosine rule, what is the correct formula for side *a*?
Answer
(A)
a^2 = b^2 + c^2 - 2bc cos A
14
In a triangle, if a = 8 cm, b = 10 cm, and angle A = 40°, find the measure of angle B (approximately):
Answer
(B)
51.3°
15
To find the area of a triangle knowing all three sides (a, b, c), which formula is appropriate?
Answer
(B)
Heron's Formula
16
If the angle is 45 degrees, what is the relationship between the opposite and adjacent sides?
Answer
(C)
Opposite = Adjacent
17
What is the area of the square on the hypotenuse of a right-angled triangle equal to?
Answer
(A)
The sum of the areas of the squares on the other two sides
18
What does '180-θ' represent in relation to the sine function?
Answer
(C)
An angle that has the same sine value as θ (acute)
19
What is the sum of the angles of a non-right-angled triangle?
Answer
(B)
180°
20
Which of the following is always true for the Law of Sines?
Answer
(A)
The longest side is always opposite the largest angle.
21
Given a triangle with sides 3cm, 4cm, and an included angle of 30 degrees, what is the area?
Answer
(B)
3cm^2
22
If side a = 3 and side b = 4, what is the length of side c (hypotenuse)?
Answer
(A)
5
23
For a triangle, given the area and two sides, which trigonometric function should be used to determine the angle?
Answer
(A)
Sine
24
In a right-angled triangle, which side is opposite to the given angle?
Answer
(C)
Opposite
25
Given the adjacent side and the hypotenuse, which function must be used?
Answer
(B)
Cosine
26
What concept is used to determine the shortest distance between a point and a line?
Answer
(C)
The perpendicular distance
27
What is the relationship between the angle of elevation and the angle of depression, assuming the horizontal lines are parallel?
Answer
(C)
They are equal.
28
If a field is in the shape of a quadrilateral with sides of 80m and 60m, a vertical post (CT) is located in one corner of the field. What steps are needed to find the height of the post?
Answer
(B)
Use trigonometric function and find the angle of elevation
29
Which trigonometric function is defined as the ratio of the opposite side to the hypotenuse?
Answer
(A)
Sine
30
If the adjacent side is 10 and the angle is 60, find the opposite side.
Answer
(B)
5
31
What is the correct formula to calculate the area of a triangle given two sides and the included angle?
Answer
(A)
Area = 1/2 * ab * sinC
32
What information is needed to calculate a bearing?
Answer
(B)
The angle between the north line and the direction
33
What trigonometric function should you use to find an angle, given the opposite and adjacent sides?
Answer
(C)
Tangent
34
If the angle of elevation from a point on the ground to the top of a building is 45 degrees, and the horizontal distance to the building is 100 meters, what is the height of the building?
Answer
(C)
100 meters
35
Which side of a right-angled triangle is opposite to the right angle?
Answer
(C)
Hypotenuse
36
Which of the following identities is correct?
Answer
(C)
sin^2(x) + cos^2(x) = 1
37
What is the value of cos(60°)?
Answer
(B)
0.5
38
A boat, C, is 10km away on a bearing of 090 degrees. Boat, B, is 6km away on a bearing of 150 degrees from the same point. What is needed to calculate the distance between the two boats?
Answer
(A)
Cosine rule
39
Which trigonometric ratio involves the opposite and adjacent sides?
Answer
(C)
Tangent
40
If the bearing of B from A is 045°, then the bearing of A from B is:
Answer
(B)
225°
41
If the bearing of point B from point A is 120°, what is the bearing of point A from point B?
Answer
(C)
300°
42
Which formula helps to determine the angle in a triangle if we know the area and the lengths of two sides?
Answer
(A)
Area = 1/2*ab*sinC, rearrange for angle
43
What is the value of tan(0°)?
Answer
(A)
0
44
The side opposite the angle you are using (θ) is called the...
Answer
(C)
Opposite
45
What does 'a' represent in Area=1/2*ab*sinC?
Answer
(B)
A side of the triangle
46
In a right triangle, which side is opposite to the right angle?
Answer
(C)
Hypotenuse
47
In the formula to calculate the area of a triangle: Area = 1/2 * ab * sinC. What do a and b represent?
Answer
(B)
Sides
48
Which one of the following can't be used to determine the area of a triangle?
