This set of Aptitude Questions and Answers (MCQs) focuses on “Height and Distance”. These questions are beneficial for various competitive exams, placement interviews, and entrance tests.

1. Which of the following options is correct with respect to sin A?

a) Hypotenuse / perpendicular

b) Base / hypotenuse

c) Perpendicular / hypotenuse

d) Hypotenuse / base

View Answer

Explanation: perpendicular / hypotenuse is correct as the formula of:

Sin A = perpendicular / hypotenuse.

2. If sin x = 1 / 2, then what will be the value of x in degree?

a) 30

b) 60

c) 45

d) 37

View Answer

Explanation: 30 is the correct answer as:

Sin 30 = \(\frac {1}{2}\)

3. Which of the following options is the correct relationship between a and b, if their measure add up to 90 degree?

a) Cos a = tan b

b) Sec a = cosec b

c) Sin a = tan b

d) Tan a = cos b

View Answer

Explanation: sec a = cosec b is correct as:

As, they sum up to 90 degree,

Sec (90 – b) = cosec b

➩ Sec a = cosec b

4. If triangle XYZ is right angled at Y, then the value of cos (X + Z) will be?

a) 0

b) 1 / 2

c) 1

d) 1 / 3

View Answer

Explanation: Given,

Angle Y = 90

Angle (X + Y + Z) = 180

➩ Angle (X + Z) = 90

Thus, cos (X + Z) = cos 90

➩ Cos 90 = 0

5. What will be the value of sin (45 + A) – cos (45 – A)?

a) 1 / 3

b) 1 / 2

c) 0

d) 1

View Answer

Explanation: As we know,

Sin (45 + A) is complementary to cos (45 – A). Also, their values are equal. Thus, when we subtract them, we get a value = 0.

6. If 0 < X < 90, then what will be the value of sec A?

a) 0

b) 1

c) < 1

d) > 1

View Answer

Explanation: > 1 is correct as sec A is always greater than 1 between 0 and 90 degree.

7. If sin (20 + X) = cos 30, then what will be the value of X?

a) 40

b) 20

c) 70

d) 50

View Answer

Explanation: As we know,

Sin 60 = cos 30

➩ Sin (20 + X) = cos 30

Thus, X = 40.

8. If sin X = \(\frac {1}{2}\) and cos Y = 1 / √2, then what will be the value of (X + Y) in degree?

a) 80

b) 90

c) 75

d) 60

View Answer

Explanation: Given,

Sin X = \(\frac {1}{2}\)

➩ Sin 30 = \(\frac {1}{2}\)

➩ X = 30

cos Y = 1 / √2

➩ Cos 45 = 1 / √2

➩ Y = 45

Thus, X + Y = 30 + 45 = 75 degree.

9. If the value of sin X = \(\frac {1}{2}\), then what will be the of cot X?

a) 1 / √2

b) √3

c) 1 / √3

d) 1 / 3

View Answer

Explanation: Given,

Sin X = \(\frac {1}{2}\)

➩ Sin 30 = \(\frac {1}{2}\)

➩ X = 30

Thus, cot X = cot 30 = √3.

10. Which of the following options are the correct pair of complementary angles?

a) 37, 53

b) 65, 15

c) 60, 120

d) 45, 55

View Answer

Explanation: Complementary angles are those which together sum up to 90 degree.

Thus, option a is correct as 37 + 53 = 90.

**More Aptitude Questions and Answers on Height and Distance:**

- Height and Distance Questions (Set 2)
- Height and Distance Questions (Set 3)
- Height and Distance Questions (Set 4)
- Height and Distance Questions (Set 5)
- Height and Distance Questions (Set 6)
- Height and Distance Questions (Set 7)
- Height and Distance Questions (Set 8)
- Height and Distance Questions (Set 9)
- Height and Distance Questions (Set 10)

To practice all aptitude questions, please visit “1000+ Quantitative Aptitude Questions”, “1000+ Logical Reasoning Questions”, and “Data Interpretation Questions”.