Height and Distance - Quiz

Q: `A man is focusing on the top of a specific object. Since which side is considered the object's height, while the adjacent side is considered the distance between the object and the man's eyes?

A. hypotenuse
B. same as adjacent side
C. opposite side
D. none of the sides

Correct Option: C
Explanation:

The height of the object is on the opposite side. It is commonly calculated using Pythagoras' theorem

(hypotenuse)²= (opposite side)² + (adjacent side)²

Q: If we know distance of the object and angle of elevation, then what is use of these data?

A. Height of the object could be found
B. Able to find whether object is moving or not
C. No use of these data
D. Able to find what type of object it is.

Correct Option: A
Explanation:

Output: Height of the object could be found by using trigonometric formula like sinθ = height of the object/distance of the object.

Q: When the height of the object is equal to the distance of its shadow, then the angle of elevation could be,

A. 60
B. 90
C. 45
D. 180

Correct Option: C
Explanation:

the trigonometric formula which tells both height and distance is tanθ which is equal to height of the object/ distance of the shadow.

Output: Since, we know that tan45° = 1 , then the angle of elevation is 45°.

Q: If the shadow of building is decreasing towards itself, then the angle of elevation is

A. Increasing
B. Decreasing
C. No change
D. None of the above

Correct Option: A
Explanation:

Output: Option A is correct.

The Length of the shadow here considered as adjacent side and we know that length of adjacent side is inversely proportional to angle of elevation. Since When the shadow is decreasing, then the angle will be increased.

Q: We know that the height and distance involve a right angled triangle, since which theorem is used to find the length of the sides of that triangle?

A. Bayes theorem
B. Pythagoras theorem
C. Angle bisector theorem
D. None of the above

Correct Option: B
Explanation:

Option B is correct.

Bayes theorem deals with probability.

Angle bisector theorem deals with triangle lonely.

Hence Pythagoras theorem only deals with right angled triangle and used to find length of sides of triangle.

Q: What is the inverse of sin??

A. Cosecant?
B. Secant?
C. Cot?
D. None of the above

Correct Option: A
Explanation:

sinθ = opposite side/hypotenuse.

Inverse and reciprocal is same so as hypotenuse/opposite side is equal to cosecantθ. Option A is correct

Q: When the angle of elevation is increased from 45

A. 50.25m
B. 100.98 m
C. 49.18m
D. 45m

Correct Option: C
Explanation: Option C is correct.

Q: A ladder leaning against a wall has an elevation angle of 60

A. 7.02 m
B. 6.5 m
C. 5.62 m
D. 6.9 m

Correct Option: D
Explanation: Let AB be the wall and BC be the ladder. Then, ACB = 60° and AC =3.45 m.

AC/BC = cos 60° = 1/2

= 2 x AC

= (2 x 3.45) m

= 6.9 m.

Q: From the given image, theta1 is called the angle of elevation, and theta2 is called,

A. angle of depression
B. angle of deviation
C. angle of dissociation
D. angle of right angled triangle.

Correct Option: A
Explanation:

It's an angle formed with the horizontal line if the line of sight is downward from the horizontal line.

Q: Two cars are parked on opposite sides of a long tower. From the cars, the angle of elevation of the top of the tower is 30

A. 158 m
B. 100.6 m
C. 136.5 m
D. 200.75 m

Correct Option: C
Explanation:

Assume the distance between the tower and the two cars is x+y.'

[adjacent side = car-to-tower distance] [opposite side = tower height]

tan = opposite side/adjacent side

Triangle 1:

tan30° = 50/x => x = 50√3

Triangle 2:

tan45° = 50/y => y = 50

SOLUTION

Distance between two cars = x + y = 503 + 50 = 50(3+1) = 50*2.732 = 136.5 m