Mathematics for IGCSE & O level - Pythagoras' Theorem And Trigonometry (Section 4)
1
If two sides of a triangle and the included angle are given, which rule is most suitable for finding the third side?
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(B)
Cosine Rule
2
If a triangle's area is known along with the lengths of two sides, what trigonometric function can be used to find the angle between those two sides?
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(A)
Sine
3
When using the formula Area = 1/2 * ab * sinC, what does 'C' represent?
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(B)
The angle opposite side c
4
If in a triangle, a = 7cm, C = 53°, and c = 8cm, how many possible triangles are there?
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(C)
2
5
Which of the following are steps to solve a trigonometric problem (in order)?
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A
B
C
D
6
In a triangle, given two sides and their included angle, which formula should you use to find the area?
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(A)
Area = 1/2 * a * b * sin(C)
7
What formula is used to calculate the area of a triangle when you know two sides and the included angle?
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(B)
Area = 1/2 * ab * sinC
8
In the context of finding lengths and angles in 3 dimensions, which method is primarily used?
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(B)
Pythagoras' theorem in right-angled triangles
9
If a boat travels 10km from a starting point north and then 6km in a southerly direction, what is the boat's final displacement from the starting point?
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(A)
4 km
10
If sinA = 0.6 and angle A is obtuse, what is the value of angle A?
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(C)
126.87°
11
If we are given the angle and the length of the hypotenuse, what ratio should we use if we are trying to find the length of the side opposite the angle?
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(A)
Sine
12
What is the value of cos(180° - θ) in terms of cos θ?
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(B)
-cos θ
13
What rule helps relate the sides of a triangle to the sines of its angles?
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(B)
Sine Rule
14
What is the value of sin(30°)?
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(B)
0.5
15
What is the general formula for the sine rule?
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(A)
a/sinA = b/sinB = c/sinC
16
In the context of a right triangle, what does the term 'opposite' side refer to?
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(B)
The side across from the angle being considered
17
Given a triangle where side a = 5 cm, side b = 8 cm, and angle C = 60 degrees, what would be the next step to find the area using Area = 1/2 * ab * sinC?
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(C)
Use sine function to calculate sin(60)
18
What steps should you follow when solving a trigonometry question?
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A
B
C
19
If the length of the shadow of a vertical pole is equal to the height of the pole, what is the angle of elevation of the sun?
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(B)
45 degrees
20
Which formulas is/are correct?
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A
B
C
21
What kind of triangle has a line of symmetry?
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(C)
Isosceles
22
What is the maximum number of solutions possible in the ambiguous case of the sine rule?
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(C)
2
23
Which trigonometric function is the ratio of the adjacent side to the hypotenuse?
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(B)
Cosine
24
Which angle has a sine value of 0.5?
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(B)
30°
25
If the angle of elevation from point A to the top of a building is 45 degrees, and you are standing 50 meters away from the building, what is the height of the building (assuming a level ground) ?
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(B)
50 meters
26
What is the name of the side of a right triangle that is opposite the right angle?
When using the sine rule to solve for an angle in a triangle, what is important to consider?
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A
B
29
What is the purpose of using trigonometric ratios (sine, cosine, tangent)?
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(B)
To relate the angles of a right triangle to the lengths of its sides
30
What are the ways to remembering SOHCAHTOA?
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(B)
Silly Old Harry Can Always Hear The Old Apple Tree Rustle Over
31
What is the value of sin(270°)?
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(C)
-1
32
Which trigonometric function is used to find the angle when you know the opposite and adjacent sides?
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(C)
Tangent
33
In a triangle, the side opposite the largest angle is:
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(B)
The largest side
34
What is the first step in solving a triangle using the Law of Sines, if two angles and a side are given?
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(B)
Calculate the third angle
35
What information do you need to solve for the sides of a right triangle using trigonometry?
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A
B
36
Which formula(s) correctly represent(s) the Pythagorean theorem?
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A
B
C
37
What are the two conditions for using the Pythagorean Theorem?
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(B)
Right triangle; know two sides
38
Which of the following scenarios might lead to the ambiguous case when using the sine rule?
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(C)
Knowing two sides and an angle opposite one of them.
39
What type of triangle is defined by the Pythagorean theorem?
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(C)
Right
40
What do you call the angle between the line of sight and the horizontal when looking up at an object?
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(B)
Angle of Elevation
41
What are the two scenarios where you can use the cosine rule?
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A
B
42
Which of the following is NOT a real-world application of trigonometry?
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(D)
Cooking Recipes
43
In a right triangle, the sine of an angle is 0.5. What is the value of the angle?
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(A)
30 degrees
44
If the angle of elevation is 30 degrees, what is the approximate ratio between the opposite side and the adjacent side?
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(A)
0.5
45
What is the value of tan(90°)?
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(C)
Undefined
46
Which is the law of sines?
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(A)
a/sinA=b/sinB=c/sinC
47
What is the hypotenuse of a right-angled triangle?
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(A)
The side opposite the right angle
48
Which trigonometric function is the inverse of the sine function?
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(A)
Arcsine
49
If the angle of depression from a point A to a point B is 30 degrees, what is the angle of elevation from B to A (assuming they are at different elevations and the ground is flat)?
