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Class 10 Maths Chapter 8 Case Based Questions - Introduction to Trigonometry

Case Study - 1

An electrician wanted to repair a street lamp at a height of 15 feet. He places his ladder such that its foot is 8 feet from the foot of the lamp post as shown in the figure below:
Class 10 Maths Chapter 8 Case Based Questions - Introduction to Trigonometry

Based on the above information give the, answer of the following questions:

Q1: The value of cos R is:
(a) 8/15
(b) 8/17
(c) 15/8
(d) 15/17
Ans: 
(b)
Explanation: 
Class 10 Maths Chapter 8 Case Based Questions - Introduction to Trigonometry


Q2: The value of cosec P is:
(a) 8/17
(b) 15/17
(c) 17/8
(d) 17/15
Ans:
c
Explanation:
 Class 10 Maths Chapter 8 Case Based Questions - Introduction to Trigonometry


Q3: The value of Class 10 Maths Chapter 8 Case Based Questions - Introduction to Trigonometry is:
(a) 17/30
(b) 30/17
(c) 0
(d) 1
Ans:
(c)
Explanation: 
Class 10 Maths Chapter 8 Case Based Questions - Introduction to Trigonometry


Q4: The value of cot P is:
(a) 15/17
(b) 17/15
(c) 8/15
(d) 15/8
Ans:
(d)
Explanation:
Class 10 Maths Chapter 8 Case Based Questions - Introduction to Trigonometry


Q5: The value of Class 10 Maths Chapter 8 Case Based Questions - Introduction to Trigonometryis:
(a) 253/136
(b) 357/136
(c) 479/136
(d) 1
Ans:
(c)
Explanation:
Class 10 Maths Chapter 8 Case Based Questions - Introduction to Trigonometry


Case Study - 2

In structural design a structure is composed of triangles that are interconnecting. A truss is one of the major types of enginnering structures and is especially used in the design of bridges and buildings. Trusses are designed to support loads, such as the weight of people. A truss is exclusively made of long, straight members connected by joints at the end of each member.
Class 10 Maths Chapter 8 Case Based Questions - Introduction to Trigonometry

This is a single repeating triangle in a truss system.

Q1: Based on the above information give the, answer of the following questions: In above triangle, what is the Length of AC?
(a) 5 ft
(b) 6 ft
(c) 8 ft
(d) 8/√3 ft
Ans:
(c)
Explanation:
Class 10 Maths Chapter 8 Case Based Questions - Introduction to Trigonometry


Q2: In above triangle, what is the length of BC?
(a) 5 ft
(b) 6 ft
(c) 8 ft
(d) 4√3ft
Ans:
(b)
Explanation: In right ΔABC,
Class 10 Maths Chapter 8 Case Based Questions - Introduction to Trigonometry


Q3: If sin A = sin C, what will be the length of BC?
(a) 2 ft
(b) 4 ft
(c) 8 ft
(d) 4√2 ft
Ans:
(b)
Explanation: Given, sinA = sinC
In right ΔABC
Class 10 Maths Chapter 8 Case Based Questions - Introduction to Trigonometry


Q4: If sin(A + B) = 1/√2 and cos(A − B) = √3/2, 0 < A + B ≤ 90, A > B then ∠A is:
(a) 45
(b) 37.5
(c) 32.5
(d) 35
Ans:
(b)
Explanation:
Class 10 Maths Chapter 8 Case Based Questions - Introduction to Trigonometry


Q5: If the length of AB doubles what will happen to the Length of AC?
(a) remains same
(b) doubles the original lengthy
(c) become three times the original length
(d) become half of the original length
Ans:
(b)
Explanation: Given AB = 2 × 4 = 8ft
Class 10 Maths Chapter 8 Case Based Questions - Introduction to Trigonometry
So, AC doubles the original length.


Case Study - 3

Soniya and her father went to meet her friend Ruhi for a party. When they reached Ruhi's place, Soniya saw the roof of the house, which is triangular in shape. She imagined the dimensions of the roof as given in the figure.
Class 10 Maths Chapter 8 Case Based Questions - Introduction to Trigonometry

Based on the above information, give the answer of the following questions:
Q1: If D is the mid-point of AC, then BD =
(a) 2m
(b) 3m
(c) 4m
(d) 6m
Ans:
(d)
Explanation:
Class 10 Maths Chapter 8 Case Based Questions - Introduction to Trigonometry


Q2: Measure of ∠A =
(a) 30
(b) 60
(c) 45
(d) None of these
Ans:
(c)
Explanation:
Class 10 Maths Chapter 8 Case Based Questions - Introduction to Trigonometry


Q3: Measure of ∠C =
(a) 30
(b) 60
(c) 45
(d) None of these
Ans: 
(c)
Explanation:
Class 10 Maths Chapter 8 Case Based Questions - Introduction to Trigonometry

 
Q4: Find the value of sinA + cosC.
(a) 0
(b) 1
(c) 1/√2
(d) √2
Ans:
(d)
Explanation:
Class 10 Maths Chapter 8 Case Based Questions - Introduction to Trigonometry


Q5: Find the value of tan2C + tan2A.
(a) 0
(b) 1
(c) 2
(d) 1/2
Ans: 
(c)
Explanation: tanC = 1, tanA = tan45 = 1 ⇒ tan2C + tan2A = 1 + 1 = 2.

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