CBSE Class 10 Mathematics Introduction to Trigonometry VBQs

Case Study Based Questions

Raj is an electrician in a village. One day power was not there in entire village and villagers called Raj to repair the fault. After thorough inspection he found an electric fault in one of the electric pole of height 5 m and he has to repair it. He needs to reach a point 1.3m below the top of the pole to undertake the repair work
On the basis of above, answer the following question

Question. When the ladder is inclined at an angle of α such that √3 tan α + 2 = 5 to the horizontal, find the angle α.
(a) 30°
(b)45°
(c) 60°
(d) 90°
Answer : C

Question. How far from the foot of the pole should he place the foot of the ladder? (Use 3 = 1.73)
(a) 2.89 m
(b) 2.14 m
(c) 3 m
(d) none of these
Answer : B

Question. In the above situation, find the value of 𝑠𝑖𝑛 ∝ 𝑐𝑜𝑠 ∝/2−𝑐𝑜𝑠 ∝ 𝑠𝑖𝑛 ∝/2
(a) 0
(b) 1
(c) 12
(d) none of these
Answer : C

Question. In the above situation if BD = 3 cm and BC = 6 cm. Find α
(a) 45°
(b) 30°
(c) 60°
(d) none of these
Answer : B

Question. If 15 cot α = 8. The value of sin α is
(a) 17/15
(b) 15/17
(c) 15/8
(d) 8/17
Answer : B

In the month of November, Akshay notices a tower built near his colony’s playground. He sees that it is being held by a wire, attached to the top of the tower. The wire makes an angle of 60°with the ground. Using these Information find the answers to the following questions

Question. What is the measure of ∠𝐶𝐴𝐵 ?
(a) 15°
(b) 25°
(c) 30°
(d) 45°
Answer : C

Question. What is the sin𝑟𝑎𝑡𝑖𝑜 of ∠𝐶𝐴𝐵 ?
(a) 0
(b) 1/2
(c) 1/√2
(d) √3/2
Answer : B

Question. What is the value of cos∠𝐴𝐶𝐵 ?
(a) 0
(b) 1/2
(c) 1/√2
(d) √3/2
Answer : B

Question. 𝑠𝑖𝑛²∠𝐶𝐴𝐵 + 𝑐𝑜𝑠²∠𝐶𝐴𝐵 =
(a) 0
(b) 1
(c) 2
(d) 3
Answer : B

Question. What is the value of tan90?
(a) 0
(b) 1
(c) 1/2
(d) not defined
Answer : D

Very Short Answer type Questions

Question. If tan 3x = sin450cos45 0 + sin300 then value of x is
Answer : 15°

Question. The value of 𝑐𝑜𝑠30 +𝑠𝑖𝑛60/1+𝑐𝑜𝑠60 𝑠𝑖𝑛30
Answer : 4√3/5

Question. If cot α = 7/8, then the value of ( 1+𝑠𝑖𝑛𝑎)(1−𝑠𝑖𝑛𝑎)/(1+𝑐𝑜𝑠𝑎 )(1−𝑐𝑜𝑠𝑎)
Answer :  49/64

Question. In a triangle ABC i, right angled at C if <A = 30⁰, AB = 40 units find BC
Answer : 20 UNITS

Question. In triangle ABC ,right angled triangled at B, AB = 5cm and <ACB = 300,then the length of the side AC is
Answer : 10

Question. If in a triangle ABC right angled at B , AB = 6 units and BC = 8 units then the value of the sinA cosC+cosAsinC
Answer : 1

Question. In right triangle ABC, right angled at B, < ACB = ∅, AB = 2 cm and BC = 1 cm then the value of sin² ∅ + tan²∅
Answer : 24/5

Question. In triangle OPQ, right angled at P, OP = 7𝑐𝑚, and the OP-PQ = 1𝑐𝑚,the value of sinQ is
Answer : 7/25

Question. In triangle ABC right angled at B if <A = <C then value of sinA sinB + cos A cosB will be
Answer : 1/√2

Question. If x = 2cos² α and y = 2sin²α +1 then the value of x + y
Answer : 3

Question. If tan β = 𝑎/𝑏 , then the value of
Answer : (a² + b²)/(a² -b²)

Question. Given that the sin𝛽 = √3/2 and the cosα = 0,then the value of β - α is
Answer : 30°

Question. The value of α and β if sin (α +2 β) = √3/2 and cos (α + 4β) = 0
Answer : α=30⁰, β=15⁰

Question. Triangle PQR is right angled at Q, if PQ = 5cm and RQ = 10cm then the value of sinP x cosP is
Answer : 2/5

Question. In triangle PQR right angled at Q, PQ = 3 cm and PR = 6cm Determine ∠ 𝑃𝑅𝑄
Answer : 30°

Question. The value of (sinα + cos α )2 + (cosα – sin α )²
Answer : 2

Question. If tanβ = 24/7 , then the value of sinβ + cosβ is
Answer : 31/25

Question. If 4tan α = 3 find the value of 5𝑠𝑖𝑛𝑎−3cos𝑎/5sin𝑎 + 2𝑐𝑜𝑠𝑎
Answer : 3/23

Question. If secα = 5/7, then the value of 1−𝑡𝑎𝑛𝑎/1+𝑡𝑎𝑛𝑎
Answer : 1/7

Question. If 8tanx = 15 then find sinx - cosx
Answer : 7/17