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:

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: 

Q2: The value of cosec P is:
(a) 8/17
(b) 15/17
(c) 17/8
(d) 17/15
Ans: c
Explanation:
 

Q3: The value of  is:
(a) 17/30
(b) 30/17
(c) 0
(d) 1
Ans: (c)
Explanation: 

Q4: The value of cot P is:
(a) 15/17
(b) 17/15
(c) 8/15
(d) 15/8
Ans: (d)
Explanation:

Q5: The value of is:
(a) 253/136
(b) 357/136
(c) 479/136
(d) 1
Ans: (c)
Explanation:

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.

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:

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,

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

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:

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

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.

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:

Q2: Measure of ∠A =
(a) 30^∘
(b) 60^∘
(c) 45^∘
(d) None of these
Ans: (c)
Explanation:

Q3: Measure of ∠C =
(a) 30^∘
(b) 60^∘
(c) 45^∘
(d) None of these
Ans: (c)
Explanation:

 
Q4: Find the value of sinA + cosC.
(a) 0
(b) 1
(c) 1/√2
(d) √2
Ans: (d)
Explanation:

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.