MCQ- Trigonometry in Measurement (Class- 9, Experience- 6)

Multiple Choice Quiz

Multiple Choice Quiz: Test Your Knowledge about Trigonometry in Measurement!

Question 1: In the context of measuring, which type of triangle plays an important role?

A. Equilateral triangle
B. Right-angled triangle
C. Isosceles triangle
D. Scalene triangle

Question 2: What is the relationship among the three sides of a right-angled triangle called?

A. Pythagorean Theorem
B. Trigonometric Ratio
C. Sine Rule
D. Cosine Rule

Question 3: According to the Pythagorean Theorem, the square on the hypotenuse is equal to what?

A. Twice the area of the base
B. The sum of the areas of the squares on the other two sides
C. The product of the other two sides
D. Half the area of the triangle

Question 4: What does trigonometry primarily deal with?

A. Circles
B. Polygons
C. Triangles
D. Parabolas

Question 5: Which of the following is the Sine of 45 degrees?

A. 1 2
B. √ 3 2
C. 1√ 2
D. √ 3

Question 6: The Cosine of 60 degrees is:

A. 12
B. √ 3 2
C. 1
D. 0

Question 7: The Tangent of 30 degrees is:

A. 1√ 3
B. √ 3
C. 1
D. √ 3 3

Question 8: What is the origin of the word ‘trigonometry’?

A. Latin
B. Greek
C. Egyptian
D. Roman

Question 9: Which ancient civilization used trigonometry for land measurement and engineering?

A. Greeks
B. Romans
C. Egyptians
D. Babylonians

Question 10: In a right-angled triangle, what is the side opposite the right angle called?

A. Base
B. Height
C. Hypotenuse
D. Adjacent

Question 11: Which side is considered the base in a right-angled triangle?

A. The horizontal side parallel to the ground
B. The vertical side
C. The hypotenuse
D. The diagonal side

Question 12: In trigonometric terms, what is the 'opposite side'?

A. The side opposite the acute angle
B. The side opposite the hypotenuse
C. The side opposite the right angle
D. The side next to the hypotenuse

Question 13: Which of the following identities is true?

A. sin²(θ) + cos²(θ) = 1
B. sin(θ)⋅cos(θ) = 1
C. tan(θ) = sin(θ)⋅cos(θ)
D. sin²(θ) - cos²(θ) = 1

Question 14: The secant of an angle is defined as:

A. 1cos(θ)
B. 1sin(θ)
C. 1tan(θ)
D. cos(θ)

Question 15: Which side is considered the height in a right-angled triangle?

A. The horizontal side parallel to the ground
B. The vertical side located on the base
C. The hypotenuse
D. The diagonal side

Question 16: What happens to the names of the sides if the triangle is turned?

A. The names remain constant
B. The names change depending on the position of the triangle
C. Only the hypotenuse changes
D. The angles change, not the sides

Question 17: To avoid confusion, how should we name the sides of a right-angled triangle?

A. Based on the length of the sides
B. In reference to the angles
C. Alphabetically
D. Based on the area of the triangle

Question 18: If the interim angle of base and hypotenuse of right-angled triangles are equal, what can be said about the ratio of the sides?

A. They will be different
B. They will be equal
C. They will be proportional to the area
D. They will be in inverse proportion

Question 19: How many different ratios can be created using any two of the three sides of a right-angled triangle?

A. Four
B. Five
C. Six
D. Seven

Question 20: Which trigonometric function is the ratio of the opposite side to the hypotenuse?

A. Sine (sinθ)
B. Cosine (cosθ)
C. Tangent (tanθ)
D. Secant (secθ)

Question 21: What does the term 'adjacent side' refer to in trigonometry?

A. The side opposite the acute angle
B. The side opposite the right angle
C. The side next to the acute angle and hypotenuse
D. The side next to the acute angle and the right angle

Question 22: If sin(θ) = 3 5, what is cos(θ) in a right-angled triangle?

A. 4  5
B. 3  4
C. 4  3
D. 5  3

Question 23: Which of the following is the Cotangent of 45 degrees?

A. 1
B. √ 3
C. 1√ 3
D. 0

Question 24: In a right-angled triangle, the opposite side of the angle θ is 4 units and the hypotenuse is 5 units. What is sin(θ)?

A. 3  4
B. 4  5
C. 5  4
D. 4  3

Question 25: What is the value of sin(90∘-θ)?

A. cos(θ)
B. sin(θ)
C. tan(θ)
D. cot(θ)

Question 26: Which trigonometric function is the ratio of the adjacent side to the hypotenuse?

A. Sine (sinθ)
B. Cosine (cosθ)
C. Tangent (tanθ)
D. Cosecant (cscθ)

Question 27: Which trigonometric function is the ratio of the opposite side to the adjacent side?

A. Sine (sinθ)
B. Cosine (cosθ)
C. Tangent (tanθ)
D. Cotangent (cotθ)

Question 28: What are the trigonometric functions for an angle θ in a right-angled triangle?

A. sinθ, cosθ, tanθ, cscθ, secθ, cotθ
B. sinθ, cosθ, tanθ, logθ, secθ, cotθ
C. sinθ, cosθ, tanθ, cscθ, secθ, cosecθ
D. sinθ, cosθ, tanθ, logθ, expθ, cotθ

Question 29: If the measure of one acute angle in a right-angled triangle is 30 degrees, what is the measure of the other acute angle?

A. 30 degrees
B. 45 degrees
C. 60 degrees
D. 90 degrees

Question 30: Which of the following represents the Pythagorean identity?

A. cos²(θ) - sin²(θ) = 1
B. tan²(θ) + 1 = sec²(θ)
C. sin²(θ) - cos²(θ) = 1
D. cot²(θ) + 1 = csc²(θ)

Question 31: What is the term for the angle formed between the line of sight and the horizontal when looking upwards?

A. Angle of depression
B. Angle of elevation
C. Acute angle
D. Right angle

Question 32: In which quadrant are both Sine and Cosine positive?

A. Quadrant I
B. Quadrant II
C. Quadrant III
D. Quadrant IV

Question 33: The Sine of 90 degrees is:

A. 0
B. 1
C. -3
D. √ 2 2

Question 34: What is the Cosine of 0 degrees?

A. 1
B. 0
C. -3
D. 1√ 2

Question 35: What is the term for the angle formed between the line of sight and the horizontal when looking downwards?

A. Angle of depression
B. Angle of elevation
C. Acute angle
D. Right angle

Question 36: The value of cos(30∘) is:

A. √ 3   2
B. 1  2
C. √ 2   2
D. 1

Question 37: What is the Pythagorean theorem used to determine in a right-angled triangle?

A. The area of the triangle
B. The perimeter of the triangle
C. The relationship between the lengths of the sides
D. The measure of the angles

Question 38: Which of the following is true for a 45° angle in a right-angled triangle?

A. sin 45° = cos 45°
B. tan 45° = 2
C. sin 45° = 0.5
D. cos 45° = 0.5

Question 39: If tan(θ) = 1, then θ is:

A. 0 degrees
B. 30 degrees
C. 45 degrees
D. 60 degrees

Question 40: Which is related with cos(θ) :

A. tan(θ)
B. cot(θ)
C. sec(θ)
D. csc(θ)

Question 41: What is the Sine of 30° in a right-angled triangle?

A. 1
B. √ 3 2
C. 1 2
D. 0

Question 42: What is the Cosine of 60° in a right-angled triangle?

A. 1
B. √ 3 2
C. 1 2
D. 0

Question 43: Which of the following is true for all θ in trigonometry?

A. sin(θ) = cos(θ)
B. tan(θ) = cot(θ)
C. sin²(θ) + cos²(θ) = 1
D. sec(θ) = csc(θ)

Question 44: What is sin^-1(1)?

A. 0
B. π 2
C. π
D. π 4

Question 45: What is the Tangent of 45° in a right-angled triangle?

A. 0
B. 1
C. √ 3
D. 1√ 3

Question 46: In a right-angled triangle, the base is 3 units and the height is 4 units. What is the length of the hypotenuse?

A. 5 units
B. 7 units
C. 6 units
D. 8 units

Question 47: In ancient times, people used the ratio between the angles and sides of a triangle to solve problems such as:

A. Calculating the area of a circle
B. Measuring the height of a tree without climbing up
C. Finding the volume of a cylinder
D. Determining the circumference of the Earth

Question 48: The word 'trigonometry' is derived from Greek words meaning:

A. Four angles and measurement
B. Three sides and calculation
C. Three sides and measurement
D. Four sides and calculation

Question 49: In a right-angled triangle, how many acute angles are there?

A. None
B. One
C. Two
D. Three

Question 50: If a right-angled triangle is turned so that the height is parallel to the ground, what happens to the base and height?

A. They remain unchanged
B. The height becomes the base and the base becomes the height
C. Only the hypotenuse changes
D. The angles change but not the sides

Question 51: What is the hypotenuse in a right-angled triangle?

A. The longest side
B. The shortest side
C. The side opposite the acute angle
D. The side parallel to the ground

Question 52: To avoid confusion, sides of a right-angled triangle should be named in reference to:

A. Their length
B. The angles they are adjacent to
C. Their position relative to the ground
D. Their distance from the hypotenuse

Question 53: The ratios of the sides of right-angled triangles with equal interim angles of the base and hypotenuse are:

A. Always different
B. Always equal
C. Proportional to the hypotenuse
D. Proportional to the area

Question 54: If the measure of the interim angles in right-angled triangles is different, what can be said about the ratios of their sides?

A. They will be equal
B. They will be different
C. They will be proportional to the perimeter
D. They will remain constant

Question 55: Which trigonometric function is the ratio of the adjacent side to the opposite side?

A. Sine (sinθ)
B. Cosine (cosθ)
C. Tangent (tanθ)
D. Cotangent (cotθ)

Question 56: Which of the following is the correct expression for the Sine of a sum of two angles?

A. sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
B. sin(A + B) = sin(A)sin(B) + cos(A)cos(B)
C. sin(A + B) = cos(A)cos(B) - sin(A)sin(B)
D. sin(A + B) = 2sin(A) + sin(B) 2

Question 57: Which trigonometric function is the ratio of the hypotenuse to the opposite side?

A. Secant (secθ)
B. Cosecant (cscθ)
C. Tangent (tanθ)
D. Cotangent (cotθ)

Question 58: An observer measures the angle of elevation to the top of a building as 30 degrees from a point 50 meters away from the base. What is the height of the building?

A. 25 meters
B. 50 meters
C. 86.6 meters
D. 43.3 meters

Question 59: Which trigonometric function is the ratio of the hypotenuse to the adjacent side?

A. Secant (secθ)
B. Cosecant (cscθ)
C. Tangent (tanθ)
D. Cotangent (cotθ)

Question 60: What is the Cotangent of an angle θ in a right-angled triangle defined as?

A.  Adjacent side  Opposite side
B.  Opposite side   Hypotenuse
C.   Hypotenuse  Adjacent side
D.   Hypotenuse  Opposite side

Question 61: If the angle of depression from a lighthouse to a boat is 15 degrees and the lighthouse is 100 meters tall, how far is the boat from the base of the lighthouse?

A. 100 meters
B. 373.2 meters
C. 267.9 meters
D. 96.6 meters

Question 62: What is the angle of elevation if a 20-meter-high tree casts a 20-meter-long shadow on the ground?

A. 45 degrees
B. 30 degrees
C. 60 degrees
D. 90 degrees

Question 63: Which trigonometric function is not a primary function but a reciprocal of another function?

A. Sine (sinθ)
B. Cosine (cosθ)
C. Tangent (tanθ)
D. Cosecant (cscθ)

Question 64: What is the secant of an angle θ in a right-angled triangle defined as?

A.   Hypotenuse  Opposite side
B.   Hypotenuse  Adjacent side
C.  Adjacent side  Opposite side
D.  Opposite side   Hypotenuse

Question 65: The term 'hypotenuse' specifically refers to which of the following in a right-angled triangle?

A. The longest side
B. The shortest side
C. The side opposite the smallest angle
D. The side adjacent to the largest angle

Question 66: In right-angled triangles, which angle is always 90 degrees?

A. The smallest angle
B. The largest angle
C. The acute angle
D. The adjacent angle

Question 67: Which of the following trigonometric functions are equal in a 45-degree angle in a right-angled triangle?

A. Sine and Cosine
B. Tangent and Secant
C. Cosine and Cotangent
D. Sine and Secant

Question 68: A ladder is leaning against a wall, forming an angle of 60 degrees with the ground. If the ladder is 10 meters long, how far is the base of the ladder from the wall?

A. 5 meters
B. 10√ 3 meters
C. 8.66 meters
D. 10 meters

Question 69: How can you measure the width of a river standing on one side using trigonometry?

A. By calculating the area
B. By using the ratio of the angles and sides
C. By measuring the height of a tree
D. By using the perimeter

Question 70: If the base and height of a right-angled triangle are both equal, what can be said about the acute angles?

A. They are both 30 degrees
B. They are both 45 degrees
C. One is 30 degrees, the other is 60 degrees
D. They are both 60 degrees

Question 71: The trigonometric function Tangent (Tan) of an angle is defined as the ratio of:

A. Opposite side to the adjacent side
B. Adjacent side to the opposite side
C. Opposite side to the hypotenuse
D. Adjacent side to the hypotenuse

Question 72: For a 30° angle in a right-angled triangle, what is the value of sin(30°)?

A. 1
B. 1 2
C. √ 3 2
D. 1√ 3

Question 73: What is the value of tan(90°)?

A. 0
B. 1
C. Undefined
D. Infinity

Question 74: If a ladder is leaning against a wall and makes a 60-degree angle with the ground, and the length of the ladder is 10 meters, how high up the wall does the ladder reach?

A. 5 meters
B. 10√ 3 meters
C. 10√ 3 2 meters
D. 10√ 3 3 meters

Question 75: An observer is standing 50 meters away from the base of a building and measures the angle of elevation to the top of the building as 30 degrees. What is the height of the building?

A. 25 meters
B. 50 meters
C. 50√ 3 3 meters
D. 50√ 3 2 meters

Question 76: If the angle of depression from the top of a cliff to a boat on the sea is 45 degrees and the cliff is 100 meters high, how far is the boat from the base of the cliff?

A. 100 meters
B. 50 meters
C. 150 meters
D. 200 meters

Question 77: The secant function is undefined for which angle?

A. 0 degrees
B. 90 degrees
C. 180 degrees
D. 360 degrees

Question 78: Which of the following is equivalent to csc(θ)?

A. 1cos(θ)
B. 1sin(θ)
C. sin(θ)
D. tan(θ)

Question 79: What is the value of tan(45∘)?