MCQ- Trigonometry for Angular Distance (Class- 9, Experience- 7)

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Multiple Choice Quiz: Test Your Knowledge about Trigonometry for Angular Distance!

Question 1: What is the radian measure of an angle?

A. 360°
B. 2π
C. θ
D. 1 radian

Question 2: 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 3: 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 4: 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 5: What does trigonometry primarily deal with?

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

Question 6: What is the relationship between arc and radian angl

A. θ = 12
B. θ = S × r
C. θ = r × S
D. θ = S + r

Question 7: What is the origin of the word ‘trigonometry’?

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

Question 8: Which ancient civilization used trigonometry for land measurement and engineering?

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

Question 9: In a right-angled triangle, what is the side opposite the right angle called?

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

Question 10: 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 11: 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 12: What is the angle measure of a perfect circle?

A. 180°
B. 360°
C. 270°
D. 90°

Question 13: What type of measurement is 360° for angles?

A. radians
B. Cubic
C. angle
D. angle

Question 14: 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 15: 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 16: 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 17: 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 18: 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 19: 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 20: 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 21: What is the definition of radian measurement?

A. Angles that are equal to a perfect circle
B. Unit of measurement of angle at center of circle
C. the angle that corresponds to a conicometer radiometer detector
D. angle that is equal to the length of the arc

Question 22: 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 23: 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 24: What is the secondary length S drawn from the center of the circle so that θ =  1  2?

A. Circle radiometer
B. Diameter of the circle
C. equal to the diameter of the circle
D. marked arc of the circle

Question 25: Which is the correct radian measure for measuring angles?

A. 2π
B. 180°
C. 360°
D. 1 radian

Question 26: 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 27: 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 28: 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 29: What is the relationship between arcs and radian measures of angles?

A. θ = S + r
B. θ = 12
C. θ = S × r
D. θ = r + S

Question 30: If θ = 90°, then how many radians is θ?

A.    1 √ 2 
B. π
C. 2π
D. 0.5

Question 31: What is the definition of radian measure of angle?

A. 1 radian = 360°
B. 1 radian = 180°
C. 1 radian = 1 cubic centimeter
D. 1 radian = 1 arc length equal

Question 32: How many radians are the angles of a circle?

A. 360°
B. 2π
C. 1π
D. 1 radian

Question 33: What is the radian measure of a complete angle of a circle?

A. 180°
B. π
C. 360°
D. 2π

Question 34: Which is the correct definition for angle measure?

A. 1 radian = 360°
B. 1 radian = 180°
C. 1 radian = 1 cubic centimeter
D. 1 radian = 1 arc length equal

Question 35: What is the definition of radian angle?

A. A unit of angle measurement that measures the length of a full angle
B. A unit of angle measurement that measures the angle made at the center of a circle
C. The unit of measure of angle equal to arc length
D. A unit of angle measurement that measures the length made from the center of a circle

Question 36: 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 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: What is the Sine of 30° in a right-angled triangle?

A. 1
B. √ 3   2​​
C.  1  2
D. 0

Question 40: 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 41: What is the value of tan(90°)?

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

Question 42: What is the definition of radian angle measurement?

A. The unit of measure of angle equal to arc length
B. A unit of angle measurement that measures the angle made at the center of a circle
C. A unit of angle measurement that measures the length of a full angle
D. A unit of angle measurement that measures the length made from the center of a circle

Question 43: What is the Cosine of 60° in a right-angled triangle?

A. 1
B. √ 3   2​​
C.  1  2
D. 0

Question 44: What is the Tangent of 45° in a right-angled triangle?

A. 0
B. 1
C. √ 3 
D.   1√ 3 

Question 45: 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 46: 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 47: 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 48: In a right-angled triangle, how many acute angles are there?

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

Question 49: 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 50: 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 51: 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 52: 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 53: 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 54: 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 55: 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 56: If an angle θ=180°, what is its radian measure?

A. 0
B.    1 √ 2 
C.  √ 3    2
D. π

Question 57: 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 58: 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 59: 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 60: 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 61: 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 62: 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 63: 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 64: 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 65: Which is the correct definition of angle measure?

A. 1 radian = 360°
B. 1 radian = 180°
C. 1 radian = 1 cubic centimeter
D. 1 radian = 1 arc length equal

Question 66: How many radians is an angle if its measure is 360°?

A. 2π
B. 1π
C. 0.5π
D. 0π

Question 67: 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 68: If θ = 180°+θ', then what is θ'?

A. 90°
B. 45°
C. 30°
D. 60°

Question 69: If an angle θ = 270°, what is its radian measure?

A. 0
B.    1 √ 3 
C. π
D.  √ 3   2

Question 70: 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 71: If an angle θ = 90°, what is its radian measure?

A.   1 √ 3 
B.    1 √ 3 
C. π
D. 0