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?
Απάντηση
(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?
Απάντηση
(A)
Sine
3
When using the formula Area = 1/2 * ab * sinC, what does 'C' represent?
Απάντηση
(B)
The angle opposite side c
4
If in a triangle, a = 7cm, C = 53°, and c = 8cm, how many possible triangles are there?
Απάντηση
(C)
2
5
Which of the following are steps to solve a trigonometric problem (in order)?
Απάντηση
A
B
C
D
6
In a triangle, given two sides and their included angle, which formula should you use to find the area?
Απάντηση
(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?
Απάντηση
(B)
Area = 1/2 * ab * sinC
8
In the context of finding lengths and angles in 3 dimensions, which method is primarily used?
Απάντηση
(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?
Απάντηση
(A)
4 km
10
If sinA = 0.6 and angle A is obtuse, what is the value of angle A?
Απάντηση
(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?
Απάντηση
(A)
Sine
12
What is the value of cos(180° - θ) in terms of cos θ?
Απάντηση
(B)
-cos θ
13
What rule helps relate the sides of a triangle to the sines of its angles?
Απάντηση
(B)
Sine Rule
14
What is the value of sin(30°)?
Απάντηση
(B)
0.5
15
What is the general formula for the sine rule?
Απάντηση
(A)
a/sinA = b/sinB = c/sinC
16
In the context of a right triangle, what does the term 'opposite' side refer to?
Απάντηση
(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?
Απάντηση
(C)
Use sine function to calculate sin(60)
18
What steps should you follow when solving a trigonometry question?
Απάντηση
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?
Απάντηση
(B)
45 degrees
20
Which formulas is/are correct?
Απάντηση
A
B
C
21
What kind of triangle has a line of symmetry?
Απάντηση
(C)
Isosceles
22
What is the maximum number of solutions possible in the ambiguous case of the sine rule?
Απάντηση
(C)
2
23
Which trigonometric function is the ratio of the adjacent side to the hypotenuse?
Απάντηση
(B)
Cosine
24
Which angle has a sine value of 0.5?
Απάντηση
(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) ?
Απάντηση
(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?
Απάντηση
A
B
29
What is the purpose of using trigonometric ratios (sine, cosine, tangent)?
Απάντηση
(B)
To relate the angles of a right triangle to the lengths of its sides
30
What are the ways to remembering SOHCAHTOA?
Απάντηση
(B)
Silly Old Harry Can Always Hear The Old Apple Tree Rustle Over
31
What is the value of sin(270°)?
Απάντηση
(C)
-1
32
Which trigonometric function is used to find the angle when you know the opposite and adjacent sides?
Απάντηση
(C)
Tangent
33
In a triangle, the side opposite the largest angle is:
Απάντηση
(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?
Απάντηση
(B)
Calculate the third angle
35
What information do you need to solve for the sides of a right triangle using trigonometry?
Απάντηση
A
B
36
Which formula(s) correctly represent(s) the Pythagorean theorem?
Απάντηση
A
B
C
37
What are the two conditions for using the Pythagorean Theorem?
Απάντηση
(B)
Right triangle; know two sides
38
Which of the following scenarios might lead to the ambiguous case when using the sine rule?
Απάντηση
(C)
Knowing two sides and an angle opposite one of them.
39
What type of triangle is defined by the Pythagorean theorem?
Απάντηση
(C)
Right
40
What do you call the angle between the line of sight and the horizontal when looking up at an object?
Απάντηση
(B)
Angle of Elevation
41
What are the two scenarios where you can use the cosine rule?
Απάντηση
A
B
42
Which of the following is NOT a real-world application of trigonometry?
Απάντηση
(D)
Cooking Recipes
43
In a right triangle, the sine of an angle is 0.5. What is the value of the angle?
Απάντηση
(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?
Απάντηση
(A)
0.5
45
What is the value of tan(90°)?
Απάντηση
(C)
Undefined
46
Which is the law of sines?
Απάντηση
(A)
a/sinA=b/sinB=c/sinC
47
What is the hypotenuse of a right-angled triangle?
Απάντηση
(A)
The side opposite the right angle
48
Which trigonometric function is the inverse of the sine function?
Απάντηση
(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)?
