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.
отговор
(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?
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(B)
A = 1/2 * a * b * sin C
3
In a right triangle, what is the relationship between the acute angles?
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(B)
They are complementary
4
Which of the following is a correct application of the Pythagorean theorem?
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(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?
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(B)
Draw a diagram
6
In a right-angled triangle, which side is opposite the right angle?
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(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?
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(D)
Area of a parallelogram = ab*sinC
8
Which of the following functions is positive in the third quadrant?
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(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?
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(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?
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(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?
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(C)
Cosine Rule
12
The angle of elevation and angle of depression are equal because:
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(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*?
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(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):
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(B)
51.3°
15
To find the area of a triangle knowing all three sides (a, b, c), which formula is appropriate?
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(B)
Heron's Formula
16
If the angle is 45 degrees, what is the relationship between the opposite and adjacent sides?
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(C)
Opposite = Adjacent
17
What is the area of the square on the hypotenuse of a right-angled triangle equal to?
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(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?
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(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?
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(B)
180°
20
Which of the following is always true for the Law of Sines?
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(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?
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(B)
3cm^2
22
If side a = 3 and side b = 4, what is the length of side c (hypotenuse)?
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(A)
5
23
For a triangle, given the area and two sides, which trigonometric function should be used to determine the angle?
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(A)
Sine
24
In a right-angled triangle, which side is opposite to the given angle?
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(C)
Opposite
25
Given the adjacent side and the hypotenuse, which function must be used?
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(B)
Cosine
26
What concept is used to determine the shortest distance between a point and a line?
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(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?
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(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?
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(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?
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(A)
Sine
30
If the adjacent side is 10 and the angle is 60, find the opposite side.
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(B)
5
31
What is the correct formula to calculate the area of a triangle given two sides and the included angle?
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(A)
Area = 1/2 * ab * sinC
32
What information is needed to calculate a bearing?
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(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?
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(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?
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(C)
100 meters
35
Which side of a right-angled triangle is opposite to the right angle?
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(C)
Hypotenuse
36
Which of the following identities is correct?
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(C)
sin^2(x) + cos^2(x) = 1
37
What is the value of cos(60°)?
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(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?
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(A)
Cosine rule
39
Which trigonometric ratio involves the opposite and adjacent sides?
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(C)
Tangent
40
If the bearing of B from A is 045°, then the bearing of A from B is:
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(B)
225°
41
If the bearing of point B from point A is 120°, what is the bearing of point A from point B?
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(C)
300°
42
Which formula helps to determine the angle in a triangle if we know the area and the lengths of two sides?
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(A)
Area = 1/2*ab*sinC, rearrange for angle
43
What is the value of tan(0°)?
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(A)
0
44
The side opposite the angle you are using (θ) is called the...
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(C)
Opposite
45
What does 'a' represent in Area=1/2*ab*sinC?
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(B)
A side of the triangle
46
In a right triangle, which side is opposite to the right angle?
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(C)
Hypotenuse
47
In the formula to calculate the area of a triangle: Area = 1/2 * ab * sinC. What do a and b represent?
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(B)
Sides
48
Which one of the following can't be used to determine the area of a triangle?
