Trigonometry MCQ Quiz - Objective Question with Answer for Trigonometry - Download Free PDF
Last updated on Jul 11, 2025
Latest Trigonometry MCQ Objective Questions
Trigonometry Question 1:
Find the angle of elevation of the top of a 250√3 m high tower, from a point which is 250 m away from its foot.
Answer (Detailed Solution Below)
Trigonometry Question 1 Detailed Solution
Given:
Height of the tower (h) = 250
Distance of the point from the foot of the tower (b) = 250 m
Formula used:
In a right-angled triangle, tan
Here, Opposite side = Height of the tower
Adjacent side = Distance from the foot of the tower
Calculations:
Let
tan
tan
⇒ tan
We know that tan(60°) =
⇒
∴ The angle of elevation is 60°.
Trigonometry Question 2:
If
Answer (Detailed Solution Below)
Trigonometry Question 2 Detailed Solution
Trigonometry Question 3:
The length of a vertical rod and its shadow are in the ratio of 2 : √12. Find the angle of elevation of the sun.
Answer (Detailed Solution Below)
Trigonometry Question 3 Detailed Solution
Given:
Length of rod : Length of shadow = 2 : √12
Formula used:
tan θ = Height of rod ÷ Length of shadow
Calculations:
⇒ tan θ = 2 ÷ √12
⇒ tan θ = 2 ÷ 2√3 = 1 ÷ √3
⇒ θ = 30°
∴ The angle of elevation of the sun is 30°.
Trigonometry Question 4:
The angle of elevation of the top of a tower from a point on the ground, which is 48m away from the foot of the tower is 30°. Find the height of the tower.
Answer (Detailed Solution Below)
Trigonometry Question 4 Detailed Solution
Given:
Horizontal distance = 48 m; angle elevation =
Formula used:
Calculations:
⇒
⇒
⇒ h =
∴ Height of the tower 16√3 m.
Trigonometry Question 5:
A ladder leaning against a wall makes an angle θ with the horizontal ground such that tan θ =
Answer (Detailed Solution Below)
Trigonometry Question 5 Detailed Solution
Given:
tan
Height of ladder from ground (opposite side) = 30 m
Formula used:
tan
Calculation:
tan
⇒ Base =
∴ The correct answer is
Top Trigonometry MCQ Objective Questions
A tree breaks due to storm and the broken part bends, so that the top of the tree touches the ground making an angle of 30° with the ground. The distance between the foot of the tree to the point where the top touches the ground is 18 m. Find the height of the tree (in metres)
Answer (Detailed Solution Below)
Trigonometry Question 6 Detailed Solution
Download Solution PDFGIVEN:
BC = 18 m
CONCEPT:
FORMULAE USED:
Tanθ = Perpendicular/Base
Cosθ = Base/Hypotenuse
CALCULATION:
Height of the tree = AB + AC
Tan 30° = AB/18
⇒ (1/√3) = AB/18
⇒ AB = (18/√3)
Cos 30° = BC/AC = 18/AC
⇒ √3/2 = 18/AC
⇒ AC = 36/√3
Hence, AB + AC = 18/√3 + 36/√3 = 54 / √3
⇒ 54/√3 × √3 /√3 (rationalizing to remove root from denominator)
⇒ 54√3 / 3 = 18√3
∴ Height of the tree = 18√3.
Mistake Point: Here, total height of tree is (AB + AC).
The above Question is previous year Question taken directly from NCERT class 10th. Correct answer will be 18√3
An aeroplane is flying at 1 PM with height of 20 m from a point on the ground. Determine the angle of elevation of aeroplane from other point 20√3 m away from the point exact below of the aero plane on the ground.
Answer (Detailed Solution Below)
Trigonometry Question 7 Detailed Solution
Download Solution PDFWe can find the angle of elevation by using the following steps:
Calculation:
Label the height difference between the two points on the ground as "h" and the horizontal distance between the two points as "d".
Use the tangent function to find the angle of elevation:
tan(θ) =
Solve for the angle of elevation:
In this case, h = 20 m and d = 20√3 m, so:
θ = 30°
So the angle of elevation is 30°.
If tan 53° = 4/3, then, what is the value of tan8°?
Answer (Detailed Solution Below)
Trigonometry Question 8 Detailed Solution
Download Solution PDFGiven:
tan 53° = 4/3
Formula Used:
tan(x – y) = (tanx – tany)/(1 + tanxtany)
Calculation:
We know, 8° = 53° - 45°
Tan8° = tan(53° - 45°)
⇒ tan8° = (tan53° - tan45°)/(1 + tan53° tan45°)
⇒ tan8° = (4/3 – 1)/(1 + 4/3 × 1)
⇒ tan8° = (1/3)/(7/3)
⇒ tan8° = 1/7
If sec2θ + tan2θ = 5/3, then what is the value of tan2θ?
Answer (Detailed Solution Below)
Trigonometry Question 9 Detailed Solution
Download Solution PDFConcept used:
sec2(x) = 1 + tan2(x)
Calculation:
⇒ sec2θ + tan2θ = 5/3
⇒ 1 + tan2θ + tan2θ = 5/3
⇒ 2tan2θ = 2/3
⇒ tanθ = 1/√3
⇒ θ = 30
∴ tan(2θ) = tan(60) = √3If the value of tanθ + cotθ = √3, then find the value of tan6θ + cot6θ.
Answer (Detailed Solution Below)
Trigonometry Question 10 Detailed Solution
Download Solution PDFGiven:
tanθ + cotθ = √3
Formula used:
(a + b)3 = a3 + b3 + 3ab(a + b)
a2 + b2 = (a + b)2 - 2(a × b)
tanθ × cotθ = 1
Calculation:
tanθ + cotθ = √3
Taking cube on both sides, we get
(tanθ + cotθ)3 = (√3)3
⇒ tan3θ + cot3θ + 3 × tanθ × cotθ × (tanθ + cotθ) = 3√3
⇒ tan3θ + cot3θ + 3√3 = 3√3
⇒ tan3θ + cot3θ = 0
Taking square on the both sides
(tan3θ + cot3θ)2 = 0
⇒ tan6θ + cot6θ + 2 × tan3θ × cot3θ = 0
⇒ tan6θ + cot6θ + 2 = 0
⇒ tan6θ + cot6θ = - 2
∴ The value of tan6θ + cot6θ is - 2.
If sec4θ – sec2θ = 3 then the value of tan4θ + tan2θ is:
Answer (Detailed Solution Below)
Trigonometry Question 11 Detailed Solution
Download Solution PDFAs,
⇒ sec2θ = 1 + tan2θ
We have,
⇒ (sec2θ)2 – sec2θ = 3
⇒ (1 + tan2θ)2 – (1 + tan2θ) = 3
⇒ (1 + tan4θ + 2tan2θ) – (1 + tan2θ) = 3
⇒ 1 + tan4θ + 2tan2θ – 1 – tan2θ = 3
⇒ tan4θ + tan2θ = 3
(cos2Ø + 1/cosec2Ø) + 17 = x. What is the value of x2?
Answer (Detailed Solution Below)
Trigonometry Question 12 Detailed Solution
Download Solution PDFFormula Used:
1/Cosec Ø = Sin Ø
Sin2Ø + Cos2Ø = 1
Calculation:
Cos2Ø + 1/Cosec2Ø + 17 = x
⇒ Cos2Ø + Sin2Ø + 17 = x
⇒ 1 + 17 = x
⇒ x = 18
⇒ x2 = 324
∴ The value of x2 is 324.
A woman is standing 30 m away from her house. An angle of elevation from the top of her is 30° towards the top of house and angle of elevation from her foot is 60° towards the top of the house. Find the total height of the house and woman.
Answer (Detailed Solution Below)
Trigonometry Question 13 Detailed Solution
Download Solution PDFGiven:
A woman is standing 30 m away from her house. An angle of elevation from the top of her is 30° towards the top of house and angle of elevation from her foot is 60° towards the top of the house
Calculation:
In ΔABC,
⇒ tan30° = AB/BC
⇒ 1/√3 = AB/30
⇒ AB = 30/√3
⇒ AB = 30√3/(√3 × √3)
⇒ AB = 10√3 m
In ΔAED,
⇒ tan60° = AE/ED
⇒ √3 = (AB + BE)/30
⇒ AB + BE = 30√3
⇒ BE = 30√3 – 10√3
⇒ BE = 20√3 m
Total height of the house = 10√3 + 20√3 = 30√3
Height of the women = CD = BE = 20√3
Total height of the house and women = 30√3 + 20√3 = 50√3
∴ Total height of the house and women is 50√3
If sec θ - cos θ = 14 and 14 sec θ = x, then the value of x is _________.
Answer (Detailed Solution Below)
Trigonometry Question 14 Detailed Solution
Download Solution PDFGiven:
secθ - cosθ = 14 and 14 secθ = x
Concept used:
Calculations:
According to the question,
⇒
⇒
⇒
⇒
∴ The value of x is
The value of:
Answer (Detailed Solution Below)
Trigonometry Question 15 Detailed Solution
Download Solution PDFGiven:
The given expression =
Formula used:
cos 67° = sin (90° - 67°) = sin 23°
sin 67° = cos (90° - 67°) = cos 23°
sin2 θ + cos2 θ = 1
sec2 θ - tan2 θ = 1
Calculation:
=
=
= sin2 23° + 1 + cos2 23° + 1
= 1 + 1 + 1
= 3
∴ The value of the given expression is 3